David Montgomery and his girlfriend’s offseason move to Detroit didn’t get off to an auspicious start … TMZ Sports has learned one of the couple’s dogs was involved in a bloody biting incident just days after the new Lions running back got settled into his new Michigan home.

According to police documents, officers were called out to Montgomery’s new Grosse Pointe Shores residence on June 4 … after his and his GF’s pitbull mix, Lola, was accused of escaping the house and attacking a smaller dog on the sidewalk.

In police body cam footage from the scene … Montgomery’s girlfriend — Tatum Causey — can be heard explaining to officers that she was in the backyard when she realized her pooch had gotten out.

“I go inside, literally opened the door and I said, ‘Anybody see Lola?'” she told an officer at the scene. “So, I’m looking in the backyard for her — she normally stays right in the backyard — but when I walk out, I see my brother carrying her.”

The owners of the dog who claimed Lola bit their pup said in an incident report that during the attack, Lola grabbed their animal’s leg and would not let go.

“I heard our dog’s leg break,” one of the complainants wrote in the documents.

The owners said they suffered bite wounds and lacerations of their own during the attack. They added that their pup was diagnosed by the vet with two leg fractures. They also claimed it required stitches.

Causey — who has a child with Montgomery — was charged with misdemeanor harboring a vicious dog over the incident … though court records show she pleaded not guilty to the count at a hearing in late June. The records show she’s due for another hearing on the matter in September.

As for Lola, Causey shared an emotional tribute post to the dog one month after the biting incident that seemed to indicate the animal had passed away.

“So many quiet days just filled with your unconditional love,” she wrote on the IG post. “You are and always will be the best. My soul dog, I love you forever and ever my Lola Bear.”