I've done a fair amount of research on this and according to the Digest Of Ohio Motor Vehicle Laws, motorized bicycle kits are illegal, no exceptions.
Ohio law does not distinguish motor-assisted bicycles from mopeds, they are the same to them.
Definition of a Motorized Bicycle
Section 4511.01H of the Ohio Revised Code defines a motorized bicycle as
any vehicle with two tandem wheels or one front and two rear wheels which is
capable of being pedaled and is also equipped with a helper motor. The law specifies
that the helper must:
- Have a piston displacement of no more than 50 cubic centimeters.
- Produce no more than one-brake horsepower.
- Propel the vehicle to a maximum speed of no greater than 20 mph on a
level surface.
Any motor-driven or motor-assisted cycle which exceeds any of these limitations is legally a motorcycle and is subject to all vehicle registrations and operator licensing requirements that apply to full-sized motorcycles.
In addition to the requirements listed above, all motorized bicycles must be
approved by the director of the Ohio Department of Public Safety as meeting
the basic equipment standards.
That is all fine, but here's the real problem...
A vehicle does not become a motorized bicycle until the Department of Public Safety includes that vehicle on its approved list. For a copy of the list of all makes and models approved for sale in Ohio as a moped.
From another OBMV source:
Just because something looks like a moped, that doesn't guarantee it is one in the eyes of the law. Only the Ohio Department of Public Safety can certify which vehicles meet state standards. You should not accept anyone else's statement that a vehicle is a moped.
...
APPROVED MODELS
In the case of manufacturers who market more than one model, only models listed below are approved by the State of Ohio. Only vehicles on this list may legally be operated as "mopeds" in Ohio.
AMF "Roadmaster"
Aspes
Balboa (Sach's)
Baretta Model 49cc
Batavus
Benelli "Blazar"
Bermuda 147F
Bermuda 147FA
Califfo
Carabella "Motomatic" 49cc only
Cimatti "City-Bike"
Clinton 50-A
Columbia "Commuter"
Columbia "Imperial"
Columbia "Medallion 2271"
Columbia "Medallion 2281"
Columbia "Model 57062"
Columbia "Model 2251"
Columbia "Model 2241"
Columbia "Motrek"
Columbia "Western Flyer"
Com Ute
Concord "XKE"
Cosmo "Blazar I"
Cosmo "Blazar II"
Cosmo "Colt I"
Cosmo "Colt II"
Derbi "C-5 Diablo"
Derbi "Laguna Sport"
Derbi "RD-50"
Derbi"S/L"
Derbi "S/L/E"
Derbi "T/T"
Eagle "1"
Eagle "3"
F. Morini
Flandria 101
Flandria 102
Gadabout
Garelli "Basic"
Garelli "Rally SL"
Garelli "Rally Sport"
Garelli "Sport"
Garelli "Super Sport"
General 5-Star
General 5-Star (Ltd. Ed)
General 5-Star ST (Min. Eng.)
General 5-Star ST (Sach's Eng.)
Hercules "P-1"
Hercules "M-4"
Honda "Hobbit"
Honda PA 50
Indian AM 1-50
Intramotor "Blanco"
Intramotor "Pinto"
Intramotor "Scout"
Italvelo
J.C. Penney "Pinto"
J.C. Penney "Swinger"
Jagar Model EB-1Z4-BA
Jawa "Automatic 120"
Jawa"120"
Jawa "210"
Jawa "210 Sport"
Jawa "Supreme 2"
Jawa Transistor 40
Jawa "X20"
Jawa "X25"
KKM Interprises, Inc. "Mopet"
Kreidler MP-9 (Flory)
Kreidler MP-19
Lambretta Eagle
Lazer Sport 50
Lem
Majestic Auto LTD. "Ankur"
Majestic Auto LTD. "Pacer"
Majestic Auto LTD. "Panther"
Malagutti "Commuter 20"
Malanca "Roxi"
Malanca "Tiger"
Marina Mobilia "Motomarina"
Monto "Autopower"
Monto "Kobra"
Monto "Mont"
Monto "Super Sport"
Motobecane
Moto Guzzi "Robin"
Motron "Medalist"
Negrini "Gazelle"
Negrini "Harvard"
Negrini "MX Sport"
Odyssey
Peugeot103L2U1
Peugeot103LSU1
Prima (Sach's)
Puch "Astro Daimler"
Puch "Astro Daimler Two-Speed"
Puch "Beta"
Puch "Cobra"
Puch "Dart"
Puch Magnum "II"
Puch Magnum "Limited LTD"
Puch Magnum "MK II"
Puch Magnum "XK"
Puch "Maxi"
Puch "Maxi II"
Puch "Maxi GN"
Puch "Maxi Luxe"
Puch "Maxi N"
Puch "Maxi Plus"
Puch "Maxi S"
Puch "Maxi Sport"
Puch "Maxi Sport LS"
Puch "Maxi Sport LS 2-speed"
Puch "Mini Maxi"
Puch "Newport"
Puch "Newport II"
Puch "Newport L"
Puch "Nostalgia"
Puch"Sport I"
Puch "Sport MKII"
Sach "Carrier I"
Sach "Carrier II"
Sach"Feugo"
Sach "G-3"
Sach "G-4"
Sach "Minor"
Sach "Mopet"
Sach "Saxy"
Sears "Free Spirit Moped
(Nos. 80800, 80810,80840)
Seville (Sach's)
Solex
Suburban (Sach's)
Sundancer (Sach's)
Tomos "A3SL"
Tomos "A-3 Bullet"
Tomos "A-3 Bullet TT"
Tomos "A-3 Golden Bullet"
Tomos "A-3 Golden Bullet TT-LX"
Tomos "Silver Bullet SL"
Trac "Blitz"
Trac "Clipper"
Trac "Eagle"
Trac "Hawk"
Trac "Olympic"
Trac "Sprint"
Vespa "Bravo"
Vespa "Ciao"
Vespa"Grande"
Vespa "Sl"
Wards Model 57008
Westlake (Sach's)
Wildfire WF-20MB
Wildfire WF-24MB
Wildfire WF-26MB
So even if you were able to put a headlight, mirror, turn signals, brake light, etc on it, unless your motorized bicycle is an actual moped manufactured of one of the exact makes/models shown above with a commercial manufacturer VIN number, you cannot apply for registration and a motorized bicycle license plate. Only the approved makes/models shown above are allowed on Ohio roads.
sources:
ODPS | BMV | Page Not Found
Moped Information