“These are disturbing allegations,’’ said Greg Bialecki, secretary of the Executive Office of Housing and Economic Development, in a prepared statement. He said the fact that McLaughlin spent so little time in Chelsea and still claimed to take almost no vacation “further indicates that our efforts to remove the former executive director and board members were the right thing to do.’’

The FBI is investigating whether McLaughlin, a former state legislator and longtime Democratic powerbroker, illegally diverted federal funds to his own use. State housing officials tried to stop payment on the checks written to McLaughlin on his last day, but he had already cashed the one for unused vacation time.

The revelations about McLaughlin’s lax work habits and questionable payments for unused vacation and sick time come amid burgeoning state and federal investigations of the housing authority, which has been taken over by a state receiver in the wake of McLaughlin’s departure and the resignation of the entire board of directors.

McLaughlin also claimed that he almost never got sick - he reported 3.5 hours of sick time in almost 12 years - an iron constitution that led him to write a check to himself for another $114,237 on his last day as payment for years of unused sick time.

Yet McLaughlin still portrayed himself as a workhorse, claiming to take so little vacation that he was eligible to sell back unused time to the authority. On the day he resigned, McLaughlin cosigned a check to himself for $81,578 for unused vacation time, a payment that would be legitimate under the terms of his contract only if he had limited himself to four vacation days annually since 2003.

“The office was just a place [McLaughlin] stopped to delegate to everyone what to do,’’ said one housing authority employee who asked for anonymity out of fear of retaliation. “He would come in 9:45 a.m. and out by 1 p.m. or 2 p.m. . . . ‘I’m meeting a guy in Methuen.’ There was always a meeting for lunch or coffee.’’

The phone records are like a diary of McLaughlin’s work life, painting a picture of an executive who was constantly on the phone but rarely stayed long in the city where he managed low-income housing. The records show he didn’t go to Chelsea at all on almost half the working days in 2011, spending 47 weekdays in Maine and Florida with his top assistant and close personal friend, Linda Thibodeau. He spent another 21 work days at out-of-state conferences from Phoenix to Miami, usually with Thibodeau.

Michael E. McLaughlin, who abruptly resigned as Chelsea housing director last month after his $360,000 salary was revealed, put in only 15 full workdays in Chelsea all year to earn his extraordinary paycheck, according to a Globe review of his work cellphone records.

Record-keeping at the authority was often shoddy: McLaughlin kept track of dozens of unused days off he claimed to have accumulated in 2011 on hand-scrawled sheets that are virtually indecipherable. The problem was compounded by the fact that the authority’s accountant shredded weekly timesheets that would have shown the work schedule of McLaughlin and others.

But Verizon Wireless cellphone bills, which report the location of each call based on the nearest cellphone tower, provide a detailed substitute for the destroyed timesheets. In urban Eastern Massachusetts, callers are seldom more than a mile from the nearest tower, meaning that bills accurately identify the town or city for all calls except those along municipal boundaries.

For a heavy cellphone user like McLaughlin, the phone bills track his movements by the hour.

For example, on Friday, April 1, McLaughlin could not have arrived in Chelsea until sometime after 9:38 a.m. because records show he was in Reading at that moment checking his voicemail and his earlier calls were all outside of the city. Over the next three hours, McLaughlin made or received eight calls from within Chelsea. But, by 2:42 p.m., McLaughlin was placing calls from Andover where Thibodeau has a condo - and from where she was also placing calls that day. McLaughlin remained in Andover for the rest of the day, phone records show.

Based on the time between his last call before arriving in Chelsea and his first call after leaving, McLaughlin could have worked at his office no more than five hours on that day.

Taken together, out of 205 nonholiday weekdays between Jan. 1 and McLaughlin’s resignation, he was in Chelsea on 106 days, but he worked fewer than 7 hours on 91 of them. Most of the 15 full work days coincided with board meetings or inspections by the US Department of Housing and Urban Development, which consistently rated the authority a “high performer’’ during McLaughlin’s tenure.

In addition to spending limited time in Chelsea, McLaughlin made relatively few calls to his office or agency employees when he was outside the city. The 2011 phone records show that he called family and friends such as Methuen Housing Authority director Ken Martin the most, with Massachusetts political figures not far behind.

McLaughlin and Lieutenant Governor Timothy Murray phoned each other more than 120 times this year, though the cellphone calls stopped after the Globe first disclosed McLaughlin’s huge salary - nearly twice the amount paid to New York City’s housing chief - in late October.