(CNN) Prosecutors with the New York district attorney's office interviewed Donald Trump's former personal attorney Michael Cohen in recent weeks as part of their investigation of the Trump Organization's handling of hush money payments, according to people familiar with the matter.

Officials from the district attorney's office, led by Cyrus Vance, interviewed Cohen at the federal prison in Otisville, New York, where he is serving a three-year sentence after pleading guilty to multiple crimes including campaign finance violations tied to payments to two women alleging affairs with Trump a decade ago. Trump has denied having affairs with the women.

The district attorney opened the investigation last month and sent subpoenas to the Trump Organization and American Media Inc. seeking documents and records relating to payments made to Stormy Daniels and Karen McDougal to silence their allegations ahead of the 2016 presidential election.

The investigation is looking into whether the Trump Organization violated a New York state law involving false business records. Investigators are exploring whether the real estate company falsified its records in describing the reimbursement to Cohen for the payments.

Prosecutors met with Cohen shortly after they opened their investigation, according to one of the people familiar with the matter. Cohen is one of several people with knowledge of the payments who would be of interest to investigators, but he has credibility issues for any potential case. Cohen pleaded guilty last year to lying to Congress about plans to build a Trump Tower in Moscow.

Lanny Davis, a lawyer for Cohen, declined to comment. A spokesman for Vance's office also declined to comment.

Marc L. Mukasey, attorney for the Trump Organization, responded, "When you lie down with dogs you wake up with fleas." When the Trump Organization was subpoenaed early last month, Mukasey called it "a political hit job."

The investigation is a sign that legal issues continue to swirl around Trump and his business. House Democrats are suing to obtain the tax and bank records of Trump and his family members. The New York state attorney general has subpoenaed Trump's banks for loan documents relating to certain Trump Organization projects.

The state investigation, which is still in the early stages, began after the US Attorney's Office for the Southern District of New York closed its own probe in July.

Cohen was the only individual prosecuted as part of the federal investigation. He pleaded guilty to paying $130,000 to Daniels to keep her from going public with her allegation before the election.

American Media Inc., publisher of the National Enquirer, signed a non-prosecution agreement with federal prosecutors for its own role in the hush money scheme. AMI admitted to making a payment of $150,000 in cooperation with some members of Trump's campaign to prevent McDougal's claims of an affair from becoming pubic.

Federal prosecutors alleged that the Trump Organization paid Cohen $420,000 to reimburse him for the $130,000 hush money payment, increasing the amount to cover taxes and a bonus. Cohen was directed to submit monthly invoices and the payments were made in installments of $35,000 over 12 months, according to prosecutors in the Cohen case. The Trump Organization accounted for the fees as legal expenses even though, prosecutors alleged, Cohen did no legal work for the company in 2017. The Trump Organization was not charged with any wrongdoing.