Drain making dripping sound after sink drains. No leaks
I have found this on many sinks while draining a little water backs up in the over fill drain and the water in there takes a little longer to drain out as it is not as open as the main drain (the deeper the water is in the basin the longer it may take to stop). About the only way to eliminate it would be to seal off the overflow drain. Some basin designs are worse than others but this is what is happening.