It's not considered your fault, but you have to pay your collision deductible for the damage. FYI, my lawfirm does the kind of lawsuit that you might file if you decided to sue the Village Green. It sucks, but the legals bills would be between $5,000-$6,000 (just my estimate from similar cases) and you probably wouldn't see any kind of settlement money for at least 1 year, more likely 2 or 3. As long as you have a police report stating that it was a hit and run, your insurance shouldn't assess any premium increase against you. I'd call your agent just to make sure they have the whole story, though, sometimes the people at insurance agencies just push paper and don't look carefully at everything.
Sorry Toby!