If the tank was leased from a propane company to the previous owner, the propane company is obligated under the law to credit the account holder any remaining product in the tank back to the lessee. So the correct answer is the propane in the tank belongs to the propane company.
Now here is where things get tricky, the propane companies’ tank is setting on your property hooked to your home, many people have tried to claim ownership in this situation, and many have failed. Because in most cases the propane company needs to be given reasonable time to remove the tank, and in most cases they are not aware of the sale of the home until after the fact.
I have been in small claims on this exact situation more times than I would care to remember and I can honestly say that I have never lost a propane tank, and on several occasions I was awarded the cost of the fuel that the new owner had used up before I was aware of the sale.
The propane company that owns the tank should be trying to make contact with you as soon as they find out that the home has sold.
The thing that really bothers me is this happens all the time and Real-estate agents know the drill on this and they always seem to leave it out because all they are interested in is turning a quick buck.
If the tank was owned by the previous owner and you purchased the tank with the home you have full right to the product in the tank.