Water is still dripping from tank connection
What can be wrong ? You have a leak. You closed a valve this probably trapped the pressure in the tank so yes it would continue to leak. If it is a large old school pressure tank it may be close to rusting out and the drip is the warning. Old pressure tanks were usually ~5+ feet tall and about 2’ Across these were referred to as diaphragm    tanks, modern tanks are much smaller and are called bladder tanks. Both tanks use air pressure to push the water out with out having the pump to turn on for a few minutes (extending the pump life). 
Bladder tanks are smaller as almost all the water gets pushed out before the pump turns back on. Bladder tanks only about 1/2 gets pushed out.  If this is just a large holding tank the water in the tank can cause a leak and would be of great concern a non pressurized tank holding water only has ~ .4 psi per foot of water. 

So what is wrong you may have a fitting that has become loose but more likely the tank is getting close to failure if no work has been done in the area and the leak recently started.