A New York financial regulator is investigating the National Rifle Association’s participation in insurance policies that cover legal costs for policyholders in self-defense shootings.

The investigation by the state’s Department of Financial Services is focused on whether the firearms-advocacy group is improperly promoting the policy and receiving commissions without proper licensing, according to a person familiar with the matter.

The department, which regulates banks and insurers, issued a subpoena on Tuesday to the NRA group asking for documents and information about the insurance program NRA Carry Guard, according to a copy of the subpoena reviewed by The Wall Street Journal. The program was launched in April.

A website for the Carry Guard program calls it “cutting-edge insurance protection for those who lawfully carry firearms” to defend against civil and criminal legal actions. Policyholders can get $250,000 to $1.5 million of insurance protection, with coverage for legal fees and access to emergency support services for self-defense cases, including an attorney-referral network.

Some gun-control advocates contend the program could encourage people to shoot others in self-defense when such a response isn’t warranted.