Can police search my car if my dads on probation and im living with him

I think that a search of your car has to be based on probable cause, with or without a warrant.  However, your father's probation causes a number of possibilities, that might allow the search when it otherwise wouldn't be proper.

If your father uses your car, especially if he has a set of keys, then he's also in possession of the car, along with you, and if there's some suspicion that he's using drugs or alcohol, the search might be permitted.  The same would be true if he were seen driving the car in a way that connected it to an incident of some sort.  Search and seizure cases, especially car search cases, depend on the "details."