Pipe behind shower head is leaking

When I took the whole shower head off, the little pipe that you attach it to was still leaking, even though the main water supply was shut off.
I tried getting a new shower head, and water still leaks out of it while the taps are turned off.
What can I do

sounds like your washers in the valve are bad.

replace the washers or the cartridge

Make sure your water is off at the shower valve itself with internal stops, or shut you main water down.

Depending on the type of shower valve you are dealing with. Single Handle or 2/3 handle. If single handle, you need to replace the cartridge within the valve.

If 2/3 handle valve, you most likely have seats and stems in that valve. your best bet is to remove the trim(handles), then remove the stems to inspect the washers at the bottom part(they are rubber and had in by a screw). After that take a flashlight and inspect the seats within the valve. If they look pitted and broken they need replaced. At this point I would take the stems and seats to match them at you nearest plumbing supplier to match them. They sell rebuild kits for most 2/3 handle shower valves. The seats do take a special tool to remove them and can be a ***** to remove.
GOOD LUCK