There is no easy "yes/no" answer here: it all depends on what you are doing and where you are doing it.

The database will automatically disconnect when the script ends or when the "dbh"-handle goes out of scope (I notice that you did not do a my $dbh).

But if you are using mod-perl, if the script reaches its end, it does not get destroyed and the database connection remains open as exit() does not work under mod-perl.

And if you are pooling your database connections under mod-perl with Apache::DBI disconnect is a no-op anyway.

As disconnect might do some cleaning up (such as rollback, ...) depending on the type of database you are using, I think it is better to do this clean-up explicitly yourself and not rely on what disconnect might or might not do under the hood itself.