In Ohio, do you work off the last date of monetary transaction or can it be last date of activity such as a file maintenance to an address change. Does money have to be deposited or withdrawn to re-establish activity?

You need to refer to Chapter 169:

§ 169.01. Definitions.

As used in this chapter, unless the context otherwise requires:

(B) (1) "Unclaimed funds" means any moneys, rights to moneys, or intangible property, described in section 169.02 of the Revised Code, when, as shown by the records of the holder, the owner has not, within the times provided in section 169.02 of the Revised Code, done any of the following:

(a) Increased, decreased, or adjusted the amount of such funds;

(b) Assigned, paid premiums, or encumbered such funds;

(c) Presented an appropriate record for the crediting of such funds or received payment of such funds by check, draft, or otherwise;

(d) Corresponded with the holder concerning such funds;

(e) Otherwise indicated an interest in or knowledge of such funds;

(f) Transacted business with the holder.