A few drips of water are normal; however, if you have a significant amount of water coming from the tub faucet when you run the shower, you most likely have a problem with the diverter. Most tub/shower faucets have a third handle or push button in the center of the faucet or a diverter that is supposed to change the water from the tub faucet to the shower head. The diverter uses a disc to close off the tub spout opening and force water to the shower assembly.
To fix the leak, you will need to disassemble and flush out the diverter to remove any debris that may be keeping the disc, button, or handle from closing. You will need to turn off the water to the faucet before attempting to replace or clean a push button or handle diverter. If you notice white calcium and mineral deposits on the diverter, you can allow it to soak overnight in vinegar and then remove the deposits with a soft brush the following day.