505.01  DOGS AND OTHER ANIMALS RUNNING AT LARGE.
   (a)   No person being the owner or having charge of cattle, horses, swine, sheep, geese, ducks, goats, turkeys, chickens or other fowl or animals shall permit them to run at large upon any public place, or upon any unenclosed lands or upon the premises of another.
(ORC 951.02)
   (b)   No owner, keeper or harborer of any female dog shall permit it to go beyond the premises of the owner, keeper or harborer at any time the dog is in heat, unless the dog is properly in leash.
   (c)   No owner, keeper, or harborer of any dog shall fail at any time to do either of the following:
      (1)   Keep the dog physically confined or restrained upon the premises of the owner, keeper, or harborer by a leash, tether, adequate fence, supervision, or secure enclosure to prevent escape.
      (2)   Keep the dog under the reasonable control of some person.
         (ORC 955.22)
   (d)   The running at large of any such animal in or upon any of the places mentioned in this section is prima-facie evidence that it is running at large in violation of this section. 
(ORC 951.02)
   (e)   (1)   Whoever violates this section is guilty of a misdemeanor of the first degree.
      (2)   In addition to the penalties prescribed in subsection (e)(1) hereof, if the offender is guilty of a violation of subsection (b) or (c) hereof, the court may order the offender to personally supervise the dog that the offender owns, keeps or harbors, to cause that dog to complete dog obedience training, or to do both. 
(ORC 955.99)