Washington (CNN) The House Oversight Committee is asking federal prosecutors in New York whether the Justice Department's policy against indicting a sitting President played any role in the decision not to indict President Donald Trump for his role in directing Michael Cohen to arrange hush-money payments to women alleging affairs during the 2016 campaign.

House Oversight Chairman Elijah Cummings, D-Maryland, sent a letter to Deputy US Attorney Audrey Strauss Friday after the Southern District of New York revealed in a letter Thursday they had it had concluded its investigation into whether anyone else would be charged in the campaign finance scheme that Cohen pleaded guilty to last year, which was one part of Cohen's three-year prison sentence he's now serving.

Federal search warrants released Thursday detailed how Trump and his allies scrambled in the final weeks of the campaign to arrange hush-money payments. The documents are the first time that federal authorities have identified Trump by name and spelled out in his involvement in the hush-money scheme.

"If prosecutors identified evidence of criminal conduct by Donald Trump while serving as President -- and did not bring charges as they would have for any other individual -- this would be the second time the President has not been held accountable for his actions due to his position," Cummings wrote. "The Office of the President should not be used as a shield for criminal conduct."

An spokesman from the Southern District of New York declined to comment on the letter. Sources have previously told CNN that as a part of the Justice Department, its prosecutors follow department guidelines.

Read More