Showerhead leaking can be due to many reasons. There are more than four reasons but not all would be relevant in every case. In most scenarios, it is just one issue. Very rarely do we get to see more than one issue prevailing at the same time and causing shower head leaking. Let us explore the vulnerabilities of the entire shower installation including the plumbing facilitating the supply of water so you can be a better judge of the problem.
Showerhead leaking is an obvious indication that there is some point in the plumbing system supplying the water that is allowing the water to flow through the installation even when you have turned off the shower. It could be a one handle or two handle shower system with provisions for cold and hot water. No matter how many handles there are, you need to know why the showerhead is leaking.
Clogged Shower Head
The simplest reason is a clogged shower head. When a showerhead is partially or substantially clogged due to lime buildup, mineral deposits and also dirt, you will have the leak. When you turn off the water supply, the water buildup in the stem will not flow out due to a lack of pressure. When you have the supply on, the pressure of the water will overcome the blockage of lime, dirt and mineral deposits.
As the pressure is withdrawn or absent abruptly, whatever amount of water has accumulated in the stem, neck and the showerhead, it will slowly drip and flow out. This is obviously a leak but the simplest of all. You would need to uninstall the showerhead, which is mostly just a patch and turn or two, and you can clean it. Install it back and see if there is any more leakage. If the pores are heavily clogged, use a pin or needle. You may use a sturdy toothpick as well. Vinegar will get rid of the lime and mineral deposits.
Washers and Valves Need Replacement
The other problems would be any of the washers or valves having gone kaput. It could be the washers in the handles, the valves in the pipes or too much water pressure which is rendering the valves and washers useless. There can always be an excess of water pressure. Seasonal changes in temperature, too high a setting of the thermostat for the water heater and sudden gushes of water due to some reason can cause washers or valves to fail, temporarily or for a sustained period of time. These valves and washers need to be changed.