To create RITA Form 37 for someone who moved, you would have created two tabs under State & Local > Ohio Cities > Ohio City Income and Deductions.  In the tab for the previous city, scroll down to "Taxpayer Physical Address, if Different (RITA) [Override]"; there, you can enter the address of the previous residence and that will print on the first line of the table.  Otherwise, PTO will use the address entered for 1040 as the default for both lines.

If you are still having problems, deleting both tabs and recreating them first with the previous residence followed by the second tab for the current residence should help.  If the order is reversed, PTO just doesn't seem to pick up the entries correctly for some reason.