Is The Overflow Tube On An Electric Water Heater Supposed To Leak?

You need to change the temperature pressure relief valve. You could try opening the valve first to get debri out of it, this may eliminate the drip. The overflow tube/ tpr valve is meant to drip if the temp or pressure gets to high and avoids possible water heater explosion. Beware, the water exiting this tube may be scalding.

Most public water systems now require a back flow preventer. If you have one (it could be at the water meter), you must have an expansion tank to keep water from discharging through the valve. Often once water is discharged, the valve gets crud on the seat and must be replaced.

IF IT WAS NOT doing it before, and YOU HAVEN"T changed the temp. Setting then the pop off needs to be changed! A PLUMBER SAID THAT!
WARNING! Turn off the water supply, and then go to a HOT WATER out let and turn it on till it quits running, LEAVE IT ON! Then and ONLY THEN open the lever on the on the hot water pop off and replace!
Any questions go to my Plumber Help Group!
Logic101

If releasing the valve does not help, look for another water heater. A heater leaking is one of the signs that could mean the end of your water heater. Water Heaters (electric) can last anywhere from 6-10 years-depending on the usage. I've already had 3 replaced.