Footage shows the officers sitting in the vehicle and kissing each other in a Tesco car park in Blackburn, Lancs.
At some point, the female officer can be seen getting out of the patrol car and walking round to the driver's side to continue kissing the other cop.
The man who filmed the clip said he was shocked at the public display of affection on Good Friday.
He said: “I was sat with my friend in the car park, I’d gone to fix my car.
“After we were done we were just parked in the supermarket car park having a little break.
“My friend noticed the police officer in his mirror and saw that a woman had got into his car. It just didn’t feel right.”
He said the pair, both working for Lancashire Police, were initially in their own cars - the male officer in a patrol car and the woman in an unmarked car.
The witness said they pulled up next to each other and were talking from car to car before the female officer got out and joined the cop in his car.
The man said: “They were kissing in the car - their faces were colliding. They were sat in the car for about 20 minutes.
“This is an on-duty police officer sitting in a car for 20 minutes doing b*gger all.
“It annoyed me. People were walking past and taking a double look into the vehicle and thinking ‘Is that really happening?’
“They were laughing and joking and kissing.
“I don’t think they should be doing it on police time, even if he was on his lunch break it looks bad. To me, it looked like an affair.”
The man said the incident lasted about half an hour.
Lancashire Police said the male officer was on duty, but the woman was not working at the time of the incident.
A spokesman for the police force described it as an “isolated incident.”
He added: “Lancashire Constabulary appreciates the impact social media videos can have on public confidence.
“This was an isolated incident involving one off duty and one on duty police officer.
“The officers have since been spoken to and apologised for their conduct and understand how this may have been interpreted, the matter is now closed.”
The officers were forced to apologise after the incident