I think I read this in an anthology, probably in the 1980s or 1990s, possibly one of the Alfred Hitchcock anthologies. At the beginning, a man is transporting a dead dog to a field to bury it. I'm not certain if it was a family pet, or one that he hit on the road. As a result of transporting the dog, he winds up with blood all along the inside of his van (and my brain keeps wanting to say it was a domestic van rather than a passenger car) and on his hands. Sometime shortly thereafter, the police pick him up on suspicion of murder, maybe of his wife, with part of the evidence being all of the blood. He explains about the dog, but when he takes them to the field, he can't find the dog. I'm not certain why they didn't test what sort of blood was in the car... maybe it was an older story, or maybe there was a twist where he was getting framed and there really was human blood in his car.
I don't remember the exact resolution, but I think it turns out that the dog wasn't as dead as he thought it was, and had managed to dig its way out and stagger a distance before finally dying, and his innocence is proven.