Can parking space be bought by the flat owner and third party

My son bought a flat on bank loan jointly with me as co-owner only a name in the document without contribution from my end. Flat is registered and possession was available. Now, to buy a car parking place, my wife made entire payment. She wishes to register the car parking place in joint name of my son and hers or joint name of myself and hers as either case one of the co-owner of flat is included. Flat vendor is hesitating, saying that it may not be legally permissible. According to the vendor, flat owners are to be the car parking owner. legal opinion therefore is sought for.