“I just don't get it, I did nothing wrong here. I was pistol-whipped,” Kilmer told police.
Kilmer and Wright both have concealed carry permits, but it is illegal to carry a firearm while intoxicated.
Kilmer refused EMSA services and was taken to a hospital by police before being taken to the Oklahoma County jail, according to the report.
Both Kilmer and Wright were released on bail.
They have been suspended from work without pay pending the police investigation, EMSA spokeswoman Lara O'Leary said.
Kilmer was hired in June 2011 and Wright was hired in November 2007, O'Leary said.
Both are members of the International Association of EMTs and Paramedics union, she said.