thanks td-ref.

according to the Interim Provisions of Shanghai Municipality on Motorbike Administration (1997, I can't find anything more recent)

It says that
Article 3
A “ motorbike” in the present Provisions refers to a bicycle that uses a small gasoline motor but can also be footpedaled.
Article 4
A motorbike shall meet the following main technical requirements:
(1)The functional volume of the gasoline motor shall not exceed 36 cubic centimeter;
(2)The maximum design speed shall not exceed 24 kilometers per hour;
(3)The main safety devices, such as the brake, the handlebar, the bell or horn, the head light and back reflector, shall be adequate equipped and in good condition; and
(4)The wheels shall be 510-660 millimeter in diameter.

and

Article 10
Motorbike owners applying for a motorbike license under Article 12 (1) of the present Provisions shall submit the application to the traffic control department under the public security bureau of the district or county where his/her permanent residentstatus is registered.
When applying for a motorbike license, motorbike owners shall provide the following:
(1) the Shanghai resident identification card;
(2) Purchase receipt or other certificates to prove lawful ownership of the motorbike;
(3) The motorbike's quality certificate issued by the manufacturer;
(4) Certificate of third party liability insurance issued by an insurance company in Shanghai; and
(5) Receipt for the payment of tax for use of vehicles.

and

Motorbike license plates shall have two types:
(1) Downtown plate;
(2) Suburban plate.
The plate shall be placed in the fixed position in front of the handlebar.
Article 12
Permanent residents in all the counties, as well as in Pudong New Area (areas beyond the Inner Ring Road), Baoshan District, Jiading District and Minhang District may apply for a suburban plate.
No more new downtown plates shall be granted.
When motorbikes bearing a downtown plate are discarded as useless, their plates will be canceled.

So I cannot find the law pertaining to motorcycles (I'm guessing thats what mine is, I would've called it a motorbike or motorcycle). On the traffic control website I can only find laws form 2001 onwards. The 1997 law came from a google search