Marilyn L. Glynn, who served as the general counsel at the Office of Government Ethics from 1997 to 2008, said the letter to the Department of Justice is significant and unusual and that if Mr. Trump intentionally filed an inaccurate disclosure last year, he may have violated the law.

But she added that the matter is now unclear — as the referral from the ethics office does not explicitly state that the agency itself has concluded there was a violation and it is hard to know exactly when Mr. Trump learned about the debt.

“What did he know and when did he know it,” she said. “At time he filed it last year, he may not have known this payment was made or that a payment was made at all.”

Mr. Trump’s disclosure of the repaid debt to Mr. Cohen did little to clear up confusion about the total size of the reimbursements. Rudolph W. Giuliani, Mr. Trump’s attorney, said earlier this month that Mr. Cohen was paid $460,000 or $470,000 from Mr. Trump, which also included money for “incidental expenses” that he had incurred on Mr. Trump’s behalf.

Mr. Giuliani said Mr. Trump started paying Mr. Cohen back through a series of monthly installments of roughly $35,000 and that those payments began last year and may have carried into this year. The filing released on Wednesday capped the amount Mr. Trump paid back to Mr. Cohen in 2017 at $250,000, leaving more than $200,000 of the amount Mr. Giuliani mentioned unaccounted for.

The disclosure did not preclude the possibility that federal investigators could determine the payment to Ms. Clifford violated campaign finance laws. If they conclude it was made with the intention of influencing the presidential campaign — making it an effective political contribution — it would violate election law, which caps individual donations to federal candidates at $5,400 per election cycle.

Candidates are allowed to spend as much as they want on their own campaigns. And, according to the filing, Mr. Trump paid Mr. Cohen back, making Mr. Cohen’s initial payment a loan. But campaign finance law treats personal loans as contributions and the $5,400 limit would have applied. Public campaign filings are also supposed to account for all loans, contributions and payments; Mr. Trump’s made no mention of the Cohen arrangement.