A careful search through the ASPPB (licensing organization) requirements for supervised experience requirements says these states do not require post-doc hours for licensure:
http://www.asppb.org/HandbookPublic/Reports/default.aspx?ReportType=SupervisedExperience
Alabama
Arizona
Indiana
North Dakota
Ohio
(Puerto Rico)
Utah
Washington State
HOWEVER, please remember that you may not stay in the same state forever! Right now there is a big problem with people trying to move jurisdictions. If you are, say, licensed in Washington without postdoc hours, then move to San Francisco, you won't be eligible for licensure because you don't have the hours. So, it makes a lot of sense to also try to get some supervised experience just in case you move to a different state.