The film stars Neeson as Frank Drebin Jr., son of Leslie Nielsen’s Detective Sergeant Frank Drebin, as he follows in his bumbling father’s footsteps and must solve a murder case to prevent the police department from shutting down.

A source confirmed their relationship to PEOPLE on July 29 amid the the stars' press tour for 'The Naked Gun' — but their flirty premiere tour had tipped people off that they might have had a romance brewing.

This after Neeson told EW earlier this month of his costar: "She's got that feistiness and innate sense of humor… And very easy on the eyes, too."