Unemployment rates fell statewide in March, according to a report released by the New York State Labor Department, Tues., Apr. 23.  The rates in Greene and Columbia counties followed the state trend. In Greene County, the unemployment rate was reported at 9.5 percent, down from 10.2 percent in February. In Columbia County, jobless rate was 7.4 percent, down from 8.3 percent during the same period. The counties in New York with the lowest unemployment rate included Tompkins, Putnam, Nassau and Rockland counties. The state reported the private sector job count increased by more than 97,000 from March 2012 to March 2013.