I work for a law firm in CT. I am on maternity leave for paid 12 weeks. I would like to extend my maternity leave for another 12 weeks. Would I be able to collect unemployment?

That will depend on CT's unemployment rules, but almost certainly not. Most if not all states offer unemployment benefits when you are unemployed through no fault of your own; opting to take an additional 12 weeks leave does not qualify as "no fault of your own". Work is available to you; you are opting not to take it. That's a disqualification for benefits anywhere I've ever heard of.