I thought that the St Louis FED was the ultimative resource for macro data, but even they don't appear to have a time series of state level unemployment numbers for the United States.
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The Bureau of Labor Statistics Local Area Unemployment series of data provides monthly figures at the state level from 1976-2014 downloadable as Excel, CSV, or images.
I looked into the following Series:
Where LAU meant not seasonally adjusted, and LAS was seasonal, with the 3,4,5,6 standing for labor force, employment, unemployment, and unemployment rate, respectively, and the 10000000000000 (I believe) indicating the region I chose (in this example, the State of Delaware).
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