Having done a lot with this in Win32::TieRegistry, I'd advice you to use separate classes for the tied hash and the object. So, for example, have a class My::Module::Hash which is what you tie the hashes to. Then just bless a reference to such a tied hash into the My::Module class.
You don't strictly have to do it this way, but it removes so much confusion that it is well worth it. Win32::TieRegistry uses the same class for each. It works pretty well but most methods have to check whether they are being called from a blessed ref to a tied hash or directly via an object. The worst case is DESTROY which gets called twice per object because of this and the way that "global destruction" works in current versions of Perl makes it complex to tell what is going on in some cases.
Perl even supports "self-tied" things, but those get very confusing and more than once this support has been broken such that simple things become infinite loops. So I say avoid that.
(but my friends call me "Tye")