‘Breed discriminatory’ policies
Simple breed discriminatory policies specify breeds of dogs that are not permitted in a particular building, town, city, county, state, province of country. Breed bans can be established at any level of authority.

Even if a state government passes law restricting BSL for the entire state, private property owners are generally free to control what types of objects and people may come onto their property. State laws prohibiting BSL only apply to local governments, and private property is not a government. Therefore, private property owners are free to institute breed-discriminatory policies, including breed bans and restrictions.
http://stopbsl.org/lawmaking/the-u-s-lawmaking-process-and-bsl/

Breeds most commonly banned are Pit Bull Terriers, Staffordshire Terriers, Rottweilers, German Shepherds, Presa Canarios, Chows Chows, Doberman Pinschers, Akitas, Wolf-hybrids, Mastiffs, Cane Corsos, Great Danes, Alaskan Malamutes, Siberian Huskies.

‘Dangerous dog’ legislation
Pit bulls are often included as part of “dangerous dog” legislation. “Dangerous dog” laws commonly contain clauses such as the following:

• any dog that, according to the records of the SPCA, Animal Control, police or other authority, or to the knowledge of the owner, has killed, injured, or aggressively harassed or pursued a person or animal.
• any dog that has killed or injured a person, a companion animal or domestic animal while running at large
• any dog that an Animal Control Officer has reasonable grounds to believe is likely to kill or
  seriously injure a person
• any dog that aggressively harasses or pursues a person or companion animal or domestic
  animal while running at large
• any dog owned, primarily or in part, for the purpose of dog fighting or that is trained for
  dog fighting
• a Pit Bull Terrier, American Pit Bull Terrier, Pit Bull,Staffordshire Bull Terrier, American Staffordshire Terrier, or any dog of mixed breeding which includes any of these breeds
• any dog which has the appearance and physical characteristics predominantly conforming to the standards for any of the above breeds

Every owner of a Dangerous Dog must ensure that the dog is not allowed off the owner’s property unless the dog is:

• on a leash
• muzzled
• under the care and control of an owner, who is 19 years of age or older
• securely confined at all times, either indoors or in an enclosure, while the dog is on the owner’s property or controlled by the owner

A breed-specific law may be introduced by a citizen of the municipality, or it may be introduced by a member of a municipal lawmaking body (e.g. city council member or county commissioner). Typically, the lawmaking body holds at least one public hearing, and reads the proposed law on up to three different dates, before holding a vote to determine whether to pass the law. If passed, the law is applied to individuals inside the municipality’s legal limits.
http://stopbsl.org/lawmaking/the-u-s-lawmaking-process-and-bsl/

City ordinances
City ordinances may include additional requirements and restrictions for owners of pit bull type dogs, such as:

• proof of public liability insurance for bodily injury to or death of any person or for damage to property owned by any person which may result from the ownership, keeping or maintenance of a pit bull
• mandatory chips for tracking ownership and place of registration
• other identification, such as color photographs of registered pit bulls
• particular reporting requirements, such as notification of the birth of offspring of a registered pit bulldog; the new address of a registered pit bulldog if the dog is moved within the city; the name and address of the new owner

Sample ordinances:
http://www.dogsbite.org/pdf/wi-antigo-pit-bull-ban-ordinance.pdf
http://www.dogsbite.org/pdf/mo-springfield-pit-bull-ordinance.pdf

Outright bans
Hundreds of cities and counties have enacted outright bans on pit bulls.

In Aurora, Colorado, for example, it is unlawful for any person to “have, own, possess, keep, exercise control over, maintain, harbor, transport, or sell within the city” any pit bull.
https://www.municode.com/library/co/aurora/codes/code_of_ordinances?nodeId=PTIICOOR_CH14AN_ARTIIDOCA

The Dog Owner’s Liability Act in the province of Ontario, Canada severely restricts the ownership of pit bulls and bans the following: breeding a pit bull; transferring a pit bull by sale, gift or otherwise; abandoning a pit bull other than to a pound operated by or on behalf of a municipality, Ontario or a designated body; importing a pit bull into Ontario; or training a pit bull for fighting.
http://www.ontario.ca/laws/statute/90d16