From the BLS: Regional and State Employment and Unemployment Summary
Unemployment rates were significantly lower in November in 18 states and stable in 32 states and the District of Columbia, the U.S. Bureau of Labor Statistics reported today. Nine states had notable jobless rate decreases from a year earlier, 2 states had increases, and 39 states and the District had no significant change. The national unemployment rate was 4.6 percent in November, down from 4.9 percent in October, and 0.4 percentage point lower than in November 2015.
…
New Hampshire and South Dakota had the lowest unemployment rates in November, 2.7 percent each. Alaska and New Mexico had the highest jobless rates, 6.8 percent and 6.7 percent, respectively.
emphasis added
Click on graph for larger image.
This graph shows the current unemployment rate for each state (red), and the max during the recession (blue). All states are well below the maximum unemployment rate for the recession.
The size of the blue bar indicates the amount of improvement. The yellow squares are the lowest unemployment rate per state since 1976.
The states are ranked by the highest current unemployment rate. Alaska, at 6.8%, had the highest state unemployment rate. Note that the lowest recorded unemployment rate in Alaska was 6.3%, so this is pretty close to the all time low.
The second graph shows the number of states (and D.C.) with unemployment rates at or above certain levels since January 2006. At the worst of the employment recession, there were 11 states with an unemployment rate at or above 11% (red).
Currently no state has an unemployment rate at or above 7% (light blue); Only four states and D.C are at or above 6% (dark blue). The states are Alaska (6.8%), New Mexico (6.7%), Louisiana (6.2%), D.C. (6.0%), and West Virginia (6.0%).