New York State regulators have issued an expansive subpoena to the Trump Organization’s longtime insurance broker, the first step in an investigation of insurance policies and claims involving President Trump’s family business, according to a person briefed on the matter.

The subpoena was served late Monday on the company, Aon, one of the largest insurance brokerage firms in the world, as part of an inquiry by the New York State Department of Financial Services.

It came just days after Michael D. Cohen, Mr. Trump’s former fixer and lawyer, indicated in congressional testimony that the Trump Organization inflated the value of its assets to insurance companies.