The National Rifle Association has long burnished its image by attracting celebrities to its board. Internal NRA documents show that two of them—actor Tom Selleck and rocker Ted Nugent—engaged in big-ticket financial transactions with the nonprofit that the NRA board didn’t approve until at least a year later.

The new disclosures come at a time when New York Attorney General Letitia Jamesis investigating myriad financial transactions between the NRA and its top officials.

Mr....