Parking in Tbilisi is permit controlled and you must purchase a permit from the Tbilisi Transport Company to use the marked zones. On-street parking, off-street car parks and reserved parking spaces are available, local signage setting max stay and parking charges.
If parked illegally, or without a permit at best you can expect a parking ticket or at worst your car will be towed and a charge of 60 GEL imposed to release the car, increasing by 10 GEL per day.
Georgia has limited disabled parking provision, however Tbilisi is well appointed and signage is clear. Parking in a designated disabled parking bay without a permit will lead to a parking ticket, or again, the possibility of having the vehicle towed away.