A tenant recently moved out of my property after submitting their 30 day notice. The 30 days ended on August 5. I noticed on August 6th that the tenant's car (not running) was still in the garage. I am wondering about any liability or legal recourse the tenant would have if I have the vehicle towed/pushed onto the street or to impound.

Check with local and state laws.  You may be liable for abandoning the vehicle yourself if you push it onto the street.

As always, check your local landlord laws before doing anything. You are likely left with two options: 1. Call a tow company and have them tow it. If it is worth anything they will probably take it, if not they may charge you. 2. Take possession of vehicle for personal gain, the process fo which will depend on local laws.