Just eye-balling the data, it doesn't seem to correlate really strongly. The recession in the early 90's seems to match, but there doesn't seem to be a strong lagging correlation between a high unemployment rate followed by a rising murder rate.
Also, the R-squared on concurrent correlation is 28%. Using a one-year lag (how well does unemployment this year predict the murder rate next year), the correlation fell to 16%. It seems that a higher murder rate in the next year is only very weakly predicted by the data.
1. The unemployment rate is in percentages and was gather from http://www.bls.gov/. An average of the calender year unemployment rate was used.
2. The murder rate is murders/100,000 individuals.