My Kenmore Washer constantly drips inside of the tub after a wash cycle has completed. I have to turn the water off after each wash to stop the washer from dripping. Do you know what could be causing this problem?

Check the screens at both ends of the fill hose connections. If they are plugged with debris, clean them out and retest. If they are clean, or it doesn't help, then your washer has a bad water inlet valve. The part number you would need and the complexity of the repair would depend on the model number of your machine.