Michigan actually has a sort of agreement with several nearby states as far as that the other states will respect the Michigan registration and sticker on a moped as effectively covering it in thier own state.
Unfortunately, Ohio isn't one of em, part of why I moved AWAY from that misbegotten state, the whole bullcrap rigamarole of title/tags/registration/emissions/inspection/insurance/whatsizehatdoyouwear just sets my teeth right on edge, and was one of the primary reasons for riding a 'ped in the first place.
I can get with registration, it keeps theft down, but they can damnwell keep the rest.
This URL is the best I can do for NY Moped Information, since The Moped Webring does not have NY listed.
Oh, and just cause I am in a mood hostile to the Police, feel free to peruse this link as well, tho normally I don't like pages that try to sell you something.
Hope alla that helps some,