No, you have no right to prevent the landlord from renting to someone with a criminal background, unless your lease itself should happen to give you some say in new or additional rentals. Otherwise, the landlord may rent to whomever he or she likes. If the new tenant steals from you, disturbs your right to quiet enjoyment, etc., you could possibly have a cause of action against the landlord (depending on the specific circumstances) and/or against the tenant--but you can't prevent the landlord from renting to this person in the first place.