That is horrible and I am so very sorry. I have a dachshund website called www.dachshundgifts.org and there is an article on there where something similar happened----it is the paranormal related artlcle. Check it out.
I had another experience as a child where a similar thing happened to my dog---the person had just left our place as a visitor. We did confront him---he thought he had hit something but wasn't sure. When we told him he had hit and killed the family pet....I can't recall what his reaction was. I was a child. We were going for a bike ride and I looked behind me and saw Sparky laying on the road and he was not moving. My experience with death at the time was very limited. I was devastated and heartbroken to say the least.
I grew up on a farm in a rural area and we just didn't leash our dogs. This was long ago and it was part of the regional culture to let your dogs be free and to run around. I had another dog that liked to chase cars and for years did and got away with it.....until one day... Don't know who hit him. He was mortally injured and we had to put him asleep.
Well, do you know where the person lives or how to get ahold of them? Tell them about it...like say hey did you realize you ran over my beloved pet the other day? See what they say.
If they ran over your dog on purpose like swerved to hit it and someone else saw it you possibly have a legal case. I doubt however if you can do anything legally.
It is possible the person didn't even realize they hit something.
If they knew it it is possible they felt so terribly horrible that they didn't have the guts to talk to you. Some people are this way.
Talking to them about it could make you more angry and sad. They might blame it on you or fail to otherwise take responsibility.
I live in an urban area now so of course leash my dog, etc, etc.
Again, I am so very very sorry! I know how much people love their pets and how heartbreaking it is when they pass.