The congressmen also pointed out that about a decade ago, the owners of Starrett City had reached an agreement to sell the complex for $1.3 billion and that Mr. Trump had praised the deal, which would have made him about $52 million. However, that deal and others to sell the complex were blocked by the housing department because federal officials were concerned that the buyers might not be able to maintain the apartments as affordable.

The lawmakers said they are now concerned that Mr. Trump’s “representatives,” through the department, could increase his profits from the complex by approving its sale, raising rents or putting “a thumb on the scales to benefit the president and his business partners when Starrett City is refinanced during the president’s term in the office.”

The men added that they also worry that Mr. Trump’s proposed budget would make steep cuts to many housing programs but “would leave the type of federal aid that flows to the owners of Starrett City mostly intact.”

The congressmen are requesting a number of documents related to Mr. Trump’s stake in Starrett City, including communications between the Trump Organization and partners of the complex, as well as communications with banks or lenders about the complex since Mr. Trump’s election. They also want communications the Trump Organization has had with the White House or the department about the complex, and records related to how much federal housing assistance Starrett City has received in the past and how the president’s potential conflicts of interest will be managed.