Thanks everyone. I think I need to strengthen my lease in the future. Lesson learned there.
@Jon Holdman: To clarify on the designated parking spot. The house is a duplex and we built a brick parking spot for each tenant off the alleyway. It is pretty much out of site from the road, but can be clearly seen by everyone who uses the alley. The other tenant (who has been there for about 3 years) was concerned because it had out of state plates and the missing wheel etc. and was the one who originally brought it up and got me thinking. . . .
I don't want to be judgmental about what people drive either, believe me I drive a 1997 Buick LeSabre that I bought from my grandma with 75,000 miles on it. The bottom is all rusty too.
When I talked to the car owner she said she was trying to save money to fix the tire. I'm pretty sure that we don't have a case in court. I doubt there are any ordinances on this but I can do some digging. And @K. Marie Poe. You are correct, I was worried about creating "house rules" after the fact. Hence my posting here to get some advice. I do hope that I can just go on faith that it will get taken care of. They just moved in and I want to be nice but firm so they don't try to get away with anything in the future . . .I also want everyone to just get along. Perhaps I am a bit idealistic that way!