I wrote about this situation in my Singletons article for the second ever issue of The Perl Review (which means its one of the free issues :).

Apache::DBI uses the concept to let many parts of the code get a database handle without knowing what anyone else is doing. If there is already a handle with the same connection details, it gives back a reference to the existing handle. Different parts of the code talking to the same database can do it by sharing the handle without even knowing it.

It's a short bit of code, and if you already have your own database layer, you may be able to stick into what you already have without much trouble.

There may be other design tricks, too, but that would take a more careful analysis of what you already have. I can't say whether or not you should make the handle a parameter to the other class. Will that class always talk to the same database as the rest of the script? Or might it connect to different databases?

Good luck :)