Hello,
I've been trying to shut down my gas water heater and can't get it to stop refilling, constant dripping from overflow pipe. I had it repaired months ago because it was constantly leaking from the pipe coming from the pressure relief valve. Plumber put a new relief valve on and for a couple weeks it wasn't leaking. But then the constant dripping started again. Had to be money going down the drain everyday so since I was getting so low on propane and can't afford to get more right now I decided to just shut it down. I turned it to off, shut off the gas and the cold water shut off valve. Still kept dripping out the overflow pipe. So I thought I should drain the tank.Tried to drain for 2 days! It would not stop draining because to my horror you could hear water coming in the tank replenishing it! So I assumed the cold water shut off valve was not shutting it off completely. So I shut down the main water supply down by the road, disconnected the cold water supply and capped it off. Turned on main only to find now you can still hear water coming from the hot water line which has no shut off valve. How can this be? I've turned off all the how water knobs under all the sinks after running them for awhile thinking maybe there was water built up in the lines and that's what was draining into the tank. Right now I have only the kitchen hot water line open and dripping but as soon as I turn that off you the water going into the hot water heater again. Do I have to cap off the hot water line on the heater too? Why won't this thing just shut down?

90% of the time the problem is a tub or shower valve and you CANNOT usually shut them off.

So the water will keep coming into the tank via the hot line and refilling the tank?

Do you have a single handle shower or tub valve? You possibly need a new cartridge for any single handle valves. If your system is older and you have gate valves installed, you should change out those for lever handle ball valves. Also if your main valve where water enters your home is a gate valve, change it to a ball valve. Gate valves are notorious for the valve stem where it enters the gate eroding. You should send a photo to this site to get help faster with less back and forth conversation. Good luck.

Yes, the tank is filling because of backflow. You need to cap off the hot outlet pipe.