The City of Suffolk has a City wide leash law on dogs.

10-43

Any person owning, having control of, or harboring any dog within the city, shall keep such dog confined to the premises of such person, unless in the custody of a responsible person. Except as otherwise specifically provided in this section, it shall be unlawful for any person owning, having control of, or harboring any dog within the city to permit such dog to run at large within the city, or to permit the dog to go upon any public street, sidewalk or right-of-way, unless it is kept secured by a leash or lead or other means of restraint not harmful or injurious to the dog and under the control of a responsible person capable of physically restraining the dog.