I've noticed that an attempt to kill a non-hostile wild animal like a deer will be counted as an assault in the crime stats. Will hired thugs still come after me for that kind of assault?

No, they won't. They come after you if you steal from a Hunter (even accidently stealing and putting it back...:dropping it before you leave the area)

But as far as i know , they have nothing to do with animals.

But why kill a non hostile animal anyway? I go around resurrecting any non hostile animals. if i see any dead:)

But it's strange that a hunter knows you stole from him but doesn't know you put it back before you left.

At first, I never wanted to do that but then I felt I was slow in making more gold and raising the smithing skill level. So I thought it was something I had to do to progress further in the game. Unless there are plenty of bears and sabre cats found in the game. I know I'd find wolves more often than those 2 animals, I think.