Check out this graph from the SF Federal Reserve Bank

and the accompanying text:

What do the data show? For the period 2001 through 2004, we find no statistically significant relationship between productivity growth and employment growth across the U.S. states. To account for possible differences in underlying productivity, employment, and output growth, we also examined the relationships in the changes in these growth rates in recent years compared to previous periods. That analysis indicates positive but generally not statistically significant correlations between changes in employment and productivity growth. The absence of a negative relationship between productivity growth and employment growth is consistent with a wide range of firms working to make long-lasting improvements in efficiency.

Indeed, it appears that the states' employment growth rates in recent years have been related to output growth, rather than to productivity growth. This can be seen in Figure 3, which shows average productivity, employment, and output growth (GSP, or gross state product) for states that had not recovered jobs lost during the recession and those with employment levels at or above pre-recession levels. Average productivity growth across these groups is virtually the same (not different statistically). Employment and output growth, on the other hand, diverge, with fast growing states posting solid job growth, while the other states on balance have had jobless recoveries. For many firms, the gains in productivity have been sufficiently large to meet demand for their products, while firms facing stronger demand have been willing to hire new workers to meet it.