Ohio Law:
Passengers [§ 4511.53(B)] A bicycle may not be used to carry more persons at one time than the number for which it is designed or equipped; an adult cyclist may carry a child in a child seat or trailer designed to carry children [§ 4511.53(B),(C)].
http://cycle-safety.com/OH-Law-Enforcement-booklet.pdf" rel="ugc nofollow noopener">cycle-safety.comOH Law Enforcement booklet.pdfOpen ↗
I've seen all kinds of small utility/cargo trailers being pulled on our Ohio roads and I have yet to see or hear of anyone cited for that.
Ohio Electric Assist Bicycle Law:
Ohio[edit] As long as the electric bicycle meets three criteria it is considered a low-speed electric bicycle, or simply a "bicycle." First, it must travel less than 20 mph on flat ground without pedaling. Second, the bicycle must have functional pedals and finally the motor must be less than 750 watts. This is the same criteria as Federal Public Law 107-319.
A low-speed electric bicycle does not require registration, insurance, license plates (tags), or a driver's license. The rules of an electric bicycle are the same as a traditional bicycle.
There is some confusion caused by Ohio interchanging the word Moped with "motorized bicycle." If a dealer sells you a bike that follows the guidelines of Federal Public Law 107-319, then you have a bicycle. If the bike has no pedals or has a higher wattage motor than 750 watts or can travel faster than 20 mph it is classified as a moped or scooter; Ohio requires tags and registration for mopeds and scooters.
en.wikipedia.orgElectric bicycle lawsOpen ↗
I know you stated that you wanted to power the trailer, but I would think 'pusher' motive power might lead to control issues.
Ohio law is currently revised to change in 2017 that will include tricycles in the motorized bicycle (liquor cycle) category.
Bicycles are legally defined as:
(G) "Bicycle" means every device, other than a device that is designed solely for use as a play vehicle by a child, that is propelled solely by human power upon which a person may ride, and that has two or more wheels, any of which is more than fourteen inches in diameter.
codes.ohio.gov4511.01Open ↗