Due to strays breeding freely, the fact that dog owners are mixed with cat owners, and many owners not registering their dogs, there are no accurate ways to tell the excact number. However, based on those who do register their pets, there are roughly 3 million owned cats and dogs, with it being almost divided evenly between the animals, and a little over a million of free-roaming dogs and cats.
Again, it's hard to tell, and those are rough estimates made by the Wasington State Federation of Animal Care and Controll Agencies Spay/Neuter Task Force, assuming your talking about the state and no DC.
499,655 observe in 2012 December
356,709 in February 2013
967,500
656,000
256,098
274,560
190,000
290,000
5,980
58,900
78,600
568,123
622,310
23,700
250,000
35,789
143,000
89,000
201,997
250,680