Bob, Ohio is the same way. They will pay to have them shot at night, but why not have archery only lottery with entrance fee to cover costs of having a qualifing test and personel to over see it.
I'm from Toledo, and the State of Ohio did have a lottery this year for "controlled Hunts" I paid my $6.00 to enter the lottery for two locations. Albeit the odds of being selected to hunt are about as likely as winning the real lottery. I would guess that for some reason your locale would rather pay a couple gun hunters rather than have the Ohio DNR control the population and make a couple of $$ in the process.
Ohio DNR - Controlled Hunts