Do psychologists have to be licensed in the state of Connecticut?  If
I get a PhD in Buddhist Psychology, do I have to pass a licensing exam
afterwards?

Dear Barbara, 

The answer to your first question is "yes". Psychologists do need a
license in the State of Conneticut. You can read more about this
license and how to get it at the Con. Licensing Center -
http://www.ct-clic.com/trantype.asp?code=846

You must have a license either to start practicing or to renew your
old license. The fee is $450; and the perrequisites are "Approved
doctoral degree in psychology; Post-doctoral work experience;
Examination for Professional Practice in Psychology; CT state law
examination". (source: http://www.ct-clic.com/detail.asp?code=1765 ).

In other words, in answer to your second question, you have to pass
examinations even if you have PhD. The schedule for state-exam is here
- http://www.dph.state.ct.us/Publications/BRS/HSR/exams.htm

The application form can be downloaded here -
http://www.dph.state.ct.us/Licensure/apps/psych.pdf (please notice:
it's a PDF file a requires "Acrobat Reader").

If you call yourself a "therapist" (and not a psychologist) you may
not have to be licensed.

Further tips on being a psychologist and passing those state-exams:

http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=UTF8&group=sci.psychology
- a discussion group with people in your condition

http://www.psychologicalscience.net/Jobs_-_Employment/more2.html - job
and postdoctoral vacancies for psychologists.

Finally, this is the site for the State's Department of Public 
Health:  http://www.dph.state.ct.us/

I hope that helped a little, please contact me with any further
questions.