There is no overflow pipe on the water heater. There is an overflow/vent pipe on the fresh water storage tank though. It is normal for this to leak water at times.
Its possible you might have some type of winterizing hot water tank drain. But that should have a valve on it. If you have such a valve it should be shut off and not leaking.
That said we move on to the water heater. This is assuming you have a water heater leak. Or a leak with something connected right at the water heater.
You could expand this concept to move on to other pressured parts of your plumbing system to troubleshoot and isolate.
I would remove the pressure relief valve and rig up a fitting you can screw in. Set up with a pressure gauge and a air filler fitting like is on an inter-tube/tire. Some plumbing stores sell them already made up.
You might have to custom adapt this using some rubber hose rated for air compressors. Using barbed to threaded fittings and hose clamps to withstand pressure.
Install your air valve/gauge in place of the relief valve. If you have bypass valves this is a little easier. Close off the bypass valves to isolate the tank from the plumbing system.
If your plumbing set up has no bypass valves, disconnect the inlet and outlet plumbing lines. Screw in appropriate sized plugs in the two tank holes. Use teflon tape and make sure they are secured. (All easier said than done).
With an air compressor or tire pump pressurize the tank to 50psi. Soap all fittings, and your plugs, to insure you have no leaks around anything screwed in. Let this sit overnight. If your pressure drops off you have a leak. If your pressure holds I would suspect the relief valve that you removed.
You could move your air valve/gauge set up to the water inlet or outlet pipe and reinstall the relief valve, to test the relief valve. Pressure up to 50psi and soap everything again. Let it set overnight again.
If you suspect the relief valve before any of this troubleshooting starts, you might just start by installing the air valve/gauge in the inlet or outlet right from the get go.
Tanks often get pin holes on the bottom as they start to corrode through. Hard to visually find in many cases. Pressurizing with air will tell you whether you have a leak for sure. Not get everything wet in the process. Using common sense and a process of elimination, you should find the problem. There are also drain valves and in some cases anode rods that are screwed into the tank and may be a source of the leak? Soap all of these while troubleshooting.
The image is my setup. It is a little more fancy than described. I have a little valve off a T so I can use the little turn wheel and open the valve to relieve pressure without unscrewing everything. That also beats holding in the little spring loaded needle valve of the "tire filler" valve shown sticking out the right side. But I think you will get the idea of the basic concept?