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.

The new action comedy stars Neeson as Lt. Frank Drebin Jr., who is following in his father’s footsteps to solve a murder case when he meets his femme fatale love interest, played by Anderson. The film is a direct sequel to the legendary comedy series.

On Monday night, the costars attended the New York City premiere of their upcoming film with their respective kids. Anderson walked the carpet with sons Dylan Jagger Lee and Brandon Thomas Lee, while Neeson was joined by his sons, Micheál Richardson and Daniel Neeson.