The Iowa police officer who fatally shot a dog in front of the pup's owners and young kids killed another dog last month ... when he ran over the pooch with his police vehicle.

Body cam footage from the aftermath of the July 13 incident shows the officer, identified by Our Quad City News as Ethan Bock, walking over to a dog lying dead in an alleyway and admitting he ran over it with his car.

Bock utters "God dammit" and then radios in the incident, saying ... "Hey, I'm 10-2. Some frickin' dog just ran out here and I smoked it."

This dog's caretakers were there when it happened -- just like the August 21 dog shooting -- and they voiced their displeasure with the officer ... telling him he shouldn't be driving through the alley.

Bock offers up two responses ... "That's why you gotta have your dog on a leash bro" ... and "You gotta have your dog restrained, man."

Later on, a man asks Bock what the procedure is for dealing with the dead dog and Bock tells him he's sorry for what happened and says Animal Control will take over.

Another officer shows up and asks if Bock's having an issue with the dog's owners and he replies ... "No, they're upset. I smoked their dog by accident."

The family told Our Quad City News they were taking the dog out to use the bathroom.

A little over 6 weeks later, Bock is on video shooting a dog in front of a parent and two kids ... when he was responding to a report of aggressive dogs trying to jump a fence to reach another dog.