On April 3, Coldwell Banker Residential Brokerage announced that a 20,000-square-foot brick Georgian Colonial property built in 1939 and located on 5.8 acres at Indian Harbor in Greenwich was on the market for $45 million. Normally, that type of announcement would rarely generate a blip of mainstream media attention, except in this case the property was purchased in 1984 by Donald Trump as the weekend home he shared with his first wife, Ivana.

Although Trump had not lived on the property since the early 1990s — Ivana acquired it as part of their 1991 divorce settlement and sold it seven years later — the news of the property’s listing created headlines all over the world. However, it has yet to create a sale. And complicating matters was having the additional attention magnify the problems in selling this property. The home’s owners, former Bear Stearns executive Robert Steinberg and his wife, Suzanne, initially listed the property in October 2014 for $54 million, then lowered it to $45 million in May 2016 before taking it off the market later that year.

In many ways, celebrity-owned real estate is the proverbial double-edged sword for real estate agents. On the plus side, a celebrity attachment to a property gives it extra added attention.

“Listing agents are wise to use and leverage any selling power they can with buyers,” observed Joshua Shuart, chairman of the marketing and sports management department at Sacred Heart University’s Jack Welch College of Business.

“It’s usually good and helpful if someone famous is listing a house,” added Linda Skolnick, a Westport Realtor with Coldwell Banker. “It can add cachet to the listing.”

On occasion, however, a popular celebrity’s fanbase can get a bit carried away in keeping tabs on their favorite star’s activity. Craig Oshrin, a Stamford-based Realtor with Coldwell Banker, recalled his experience three years ago in selling a Fairfield residence owned by tennis star James Blake.

“Some calls were legitimate, but I would have to weed through some B.S. calls,” he said, noting that many inquiries came from Blake’s fans who were more interested in getting a peek at his lifestyle than making a serious inquiry on the property. Oshrin noted that taking an appointment-only approach to celebrity real estate helps keep the fans away. “This ensures we get the discerning, serious and qualified buyer,” he added.

Still, Oshrin’s case seemed to be the exception rather than the rule. Jim Gricar, general sales manager for Rye Brook-headquartered Houlihan Lawrence, noted that most celebrity fans do not go to the extreme of checking out their favorite star’s listed home.

“Most people don’t look at homes that are more expensive than they would purchase,” he said. “I find people respectful of giving a celebrity space in terms of seeing them.”

But what happens when the celebrity has lost the respect of the public, or worse? In Fairfield County, disgraced movie mogul Harvey Weinstein hurriedly sold off his three Westport properties after his career was derailed by multiple allegations of sexual misconduct. But buyers were not exactly clamoring for Weinstein’s residences: one was sold at a reduced price and the other two were adjacent properties acquired by a real estate investor who owned four other homes on the same street.

“Buyers do not want to be affiliated with someone who is notorious,” said Skolnick.

“If someone is perceived as polarizing, it could hurt the price because no one might want to touch the property,” said Oshrin.

Shuart pointed out that stars with image problems who reduce the price on their property or seem to be unable to secure a quick sale face a double whammy: a house lingering on the market and a reinforcement of their bad publicity. “When we see that, it is sort of like saying, ‘What’s going on here?’” he said.

Another local celebrity home that sold after a lengthy period on the market and a not-small price reduction was Cyndi Lauper’s Stamford estate, which sold in January after being listed for nine months for $804,625 — a drop from the original $1.25 million price.

Real estate experts did not see that as an indictment of Lauper’s diminished popularity, but as a reflection of luxury housing values. “Being reduced just means re-evaluating market value,” said Skolnick. “Whether you are a celebrity or a regular citizen, figuring out the market value and price is often difficult.”

“Whether a home is owned by a celebrity or a noncelebrity, the market determines what the value is,” said Gricar.

And Shuart noted that being owned by a celebrity is no guarantee that a property will be snatched up at the asking price, let alone inspire a bidding war. “In Connecticut, celebrity homes sit on the market a lot longer than the average home,” he said. “That is partly due to the price. But it doesn’t help if it’s taken on and off the market or if the price shifts around dramatically.”