Section 3.4 of the Zoning Ordinance establishes an animal density standard for the keeping of animals where no commercial activity is involved, as long as they are cared for in a manner that does not create a public nuisance or health problem.
In Rural zoning districts (e.g. the AG, AE, and FR), there is no limit on the number of animals, including cats and dogs.
In Residential districts, there are maximums for parcels that are less than 0.5 acre in size, i.e., three dogs or cats (over six months of age). For specific detail and additional restrictions, you should always check the Zoning Ordinance.