"InactiveDestroy" (boolean) The "InactiveDestroy" attribute can be used to disable the database engine related effect of DESTROYing a handle (which would normally close a pre-pared statement or disconnect from the database etc). The default value, false, means a handle will be fully destroyed when it passes out of scope.

It says the above in the DBI docs. If DBD::mysql isn't disconnecting connections when the database handle goes out of scope it is probably a bug.