Joseph Hudak of Country Weekly gave the single a "B+", saying that "It's a clever concept, elevated to near greatness by its sheer originality." He praised Urban's "earnest" vocals, and said that "the production is slick and alive—though not necessarily squarely 'country'." Kevin John Coyne of Country Universe gave it an identical rating, saying that he did not believe its storyline, but said that "Keith Urban’s heartfelt delivery and careful choice of what lines to emphasize keep the proceedings grounded. He’s so effective at capturing the feeling of falling in love that the specifics of the event surrounding the moment are appropriately secondary to the emotions at play." Thom Jurek of AllMusic wrote that "The muted drum loop that fuels the shimmering 'Cop Car,' is layered in atmospherics worthy of Achtung Baby, but the melody is pure country."
Sam Hunt—who co-wrote the song originally—recorded his version of it on his debut album Montevallo, which was released on October 27, 2014.
Hunt explains that the reason he included the song on his album is because "After writing the songs on the record, it was like a movie, and "Cop Car" was a pivotal scene in that movie. Even though Keith Urban had recorded it, I felt it still had a place on the record."