During the height of President Bill Clinton’s Monica Lewinsky scandal, a White House maid entered the bedroom to clean and was shocked to find the president and first lady’s bed covered in blood.

The blood belonged to the president, who said publicly that he “hurt himself running into the bathroom door in the middle of the night.”

But the White House residence staff believed differently. As one worker told author Kate Anderson Brower, “We’re pretty sure [Hillary Clinton] clocked him with a book.”

“There were at least 20 books on the bedside table for his betrayed wife to choose from,” Brower adds, “including the Bible.”

For “The Residence,” political journalist Brower interviewed more than 100 former members of the notoriously secretive White House residence staff, as well as former first ladies Laura and Barbara Bush and Rosalynn Carter and several former first children, for an intimate look at the personal sides of our presidents.

Here are some of their tales.

Bill Clinton

“The couple sometimes got into pitched battles, shocking the staff with their vicious cursing, and sometimes they went through periods of stoney silence,” writes Brower.

Florist Ronn Payne recalls seeing two butlers listening through the door to a “vicious” argument in the West Sitting Hall.

“All of a sudden, he heard the first lady bellow, ‘goddamn bastard!’ at the president — and then he heard someone throw a heavy object across the room. The rumor among the staff was that she threw a lamp.”

The battles increased throughout the Lewinsky scandal, and White House staffers had a front-row seat.

While the public didn’t learn of Clinton’s affair until January 1998, staffers at the White House had been watching it happen since 1995.

“The butlers saw the president and Lewinsky in the family movie theater, and the two of them were seen together so frequently that the workers started letting one another know when they’d had a Lewinsky sighting,” Brower writes.

The president paid for his indiscretions not just publicly, but at home as well.

“For three or four months in 1998,” Brower writes, “the president slept on a sofa in a private study attached to their bedroom on the second floor. Most of the women on the residence staff thought he got what he deserved.”

John F. Kennedy

While staffers had to awkwardly watch President Clinton cavorting with Lewinsky, at least no one was naked at the time.

The same can’t be said for the dalliances of President John Kennedy.

First lady Jackie Kennedy spent long getaways at the couple’s Virginia farm, and when the wife was away, the president played, swimming in the nude in the White House pool “with his female paramours, some of whom worked as secretaries in the White House.”

One staffer who came by to work on the pool got an unexpected eyeful.

“When he opened the pool door, he was shocked to see Kennedy adviser and close friend Dave Powers sitting by the pool — naked — with two of Kennedy’s secretaries.” The staffer ran out, and the incident was never mentioned.

It was well known among staffers that whenever Jackie was away, they were to avoid the second floor of the White House. Sometimes, however, it was unavoidable, as with one staffer who, Brower writes, “saw a naked woman walking out of the kitchen when he went upstairs to see if the gas was turned off.”

Not all of the staff’s Kennedy memories are sordid, though, as staffers during JFK’s administration were witness to some of the saddest presidential events of the last half-century.

When the first couple lost their 2-day-old son Patrick in August 1963, staffers scurried to rid the house of painful artifacts before Jackie returned.

“The second Patrick died, we got up there as fast as we could and took everything out,” said head housekeeper Anne Lincoln.

“They didn’t want the president and first lady to be reminded of their gut-wrenching loss when they returned,” writes Brower. “[Chief usher] J.B. West called the carpenter’s shop . . . and ordered them to get rid of the rug, crib and curtains in the blue-and-white nursery.”

When the first lady — and the nation — suffered another devastating loss three months later, it was Nanny Maud Shaw who broke the news of their father’s death to John-John and Caroline Kennedy, telling them their father was shot and that “God has taken him to heaven because they just couldn’t make him better in a hospital.”

Jimmy Carter

While Carter was president for just one term, his three adult sons saw to it that the White House was filled with enough bong smoke for two, as Payne said he would “regularly have to move bongs” from their rooms.

But all the weed in the world couldn’t relieve the stress of Carter’s presidency. When he lost his bid for re-election after a term marked by the 444-day Iranian hostage crisis, the staff saw firsthand the toll that world events took on the president and his family.

“They sobbed for two weeks” after he lost the election, said Payne. “I mean uncontrollably. You couldn’t go to the second floor without hearing it.”

Lyndon Johnson

Residence staffers who served under LBJ remember him for the nightmare that consumed his administration — his obsession with hot, powerful showers.

At his previous residence, Johnson had a special shower installed with “water charging out of multiple nozzles in every direction with needlelike intensity and a hugely powerful force. One nozzle was pointed directly at the president’s penis, which he nicknamed ‘Jumbo.’ Another shot right up his rear.”

White House engineers had to send a team to Johnson’s previous home to study the elaborate device, and determined that the shower Johnson desired would require “laying new pipe and putting in a new pump,” at a cost of tens of thousands of dollars. Johnson “demanded that the military pay for it,” and the money was taken from “classified funds that were supposed to be earmarked for security.”

Johnson, who sometimes tested the shower in front of staffers while stark naked, wanted the shower so hot that [the steam from the tests] “regularly set off the fire alarm.”

Over the years, they tested five different showers, all regarded as ineffective by the president, and even had “a special water tank installed with its own pump to up the pressure. The pumps sprayed hundreds of gallons of water per minute — more than a fire hose. Still not good enough.”

Plumbing foreman Reds Arrington spent five years trying to perfect the shower, and was driven so mad by Johnson’s demands that “he was even hospitalized for several days because of a nervous breakdown.”

Ronald Reagan

The relationship between Ronald and Nancy Reagan was a curious one. White House staffers had a front-row seat.

Usher Nelson Pierce recalls bringing some bags up to the couple’s room and having Nancy Reagan berate the president of the United States as he stood there shocked.

“She cussed him out for having the TV on,” he recalls in the book. “He said, ‘Honey, I’m just watching the news.’ As soon as she opened the door, she was into him like you wouldn’t believe.

Right in front of me. He was watching the 11 o’clock news. She thought he should be asleep.”

Perhaps no White House resident in the last half-century intimidated the residence staff like Nancy Reagan, who micromanaged with an iron fist and whom Payne referred to as “spoiled rotten.”

During preparations for a state dinner, executive pastry chef Roland Mesnier brought Mrs. Reagan dessert options while she ate lunch with the president.

After rejecting the third option she was brought, the president said, “Honey, leave the chef alone. That’s a beautiful dessert. Let’s do that.”

“ ‘Ronnie, just eat your soup. This is not your concern,’ she said. He looked down at his bowl and finished his soup without another word.”

When she finally decided on an elaborate series of sugar baskets for the guests, Mesnier informed her that the idea was too elaborate to produce in the time allotted, saying, “I only have two days left until the dinner.”

“She smiled and tilted her head to the right. ‘Roland, you have two days and two nights before the dinner.’ ”

While the president himself is remembered as always friendly and chatty with the staff — almost too much, as they had to slip away quietly if they saw him to avoid “getting trapped in a long conversation” — the first lady sought to limit this contact as best she could.

“She’d keep him the way she thought he should be,” said White House painter Cletus Clark. “She didn’t want him to associate with the help.”

George H.W. Bush

The first President Bush and his wife, Barbara, are far and away the first couple that best endeared themselves to the staff, always viewed as friendly and sincere.

“Residence workers’ devotion to President George H.W. Bush was more than customary — it was genuine, almost profound,” writes Brower.

The Bushes, unlike almost all other first families, encouraged workers to go home early rather than wait for them to call it a night and clearly regarded the staff as family.

They were also forgiving in situations that “would have enraged other presidents.”

While playing horseshoes, President Bush requested bug spray from a staffer, and “the worker [accidentally] sprayed the president from head to toe . . . with a container of industrial strength pesticide.”

By the time they got him to a doctor, “the president’s face was already red,” and he had to be “decontaminated in the shower.”

Once out of danger, the president said simply, “OK, we just want to get back to our horseshoe tournament.” No one lost their job, or was otherwise disciplined, for the incident.

Barack Obama

As a couple who had “only recently finished paying off their student loans” when Barack was elected president, the Obamas were very uncomfortable at first with being waited on hand and foot, causing a “certain distance between the staff and the new president.”

“‘With the Bushes, they wanted you to feel close to them,’ chief usher [Stephen] Rochon said. ‘With the Obamas, ‘You had to keep it completely professional.’ ”

In time, though, the first family grew closer with the staff, at least in part due to the bond created by race.

“Butler James Jeffries said there’s an unspoken understanding and respect between the Obamas and the largely African-American butler staff about the realities of being black in America,” writes Brower. “President Obama acknowledged this when he said that part of the butlers’ warmth to his family was because ‘they look at Malia and Sasha and they say, “Well, this looks like my grandbaby, or this looks like my daughter.” ’ ”

Usher Worthington White had to drop off papers for the president during the couple’s first night in the White House, after the inaugural balls.

Approaching their room, White heard the new president say, “I got this, I got this. I got the inside on this now.” Then, “the music picked up, and it was Mary J. Blige.”

The first couple, now dressed down — the first lady wore sweats and a T-shirt — were dancing to Blige’s hit, “Real Love.”

“‘I bet you haven’t seen anything like this in this house, have you?’ the president asked as the first couple danced.

“‘I can honestly say I’ve never heard any Mary J. Blige being played on this floor,’ White replied.”