Ohio murder numbers since 1960.
http://drc.ohio.gov/Public/capital.htm
The number of murders in Ohio were a lot higher when the death penalty was not enforced with the numbers going to a high of 952 murders in 1974. Also, the number of murders seemed to hover around 800 per year in the 70s where there was no death penalty enforced and appear to be in the range of 550-650 murders per year in 1980s where no death penalties were enforced either.
The numbers remained pretty high into the early 1990s. The first execution did not happen until 1999, which coincides with an all time low for murders in Ohio at 397.
In the decade afterwards, the average number for murders in Ohio appear to float around 520 murders per year with the high being 590 murders in 2005.
Now I'm not saying that the death penalty reduces the number of murders, but what you're stating doesn't seem to be the case in Ohio. Do you have any research or articles that show your point?