99% sure that Luna here is a lefty. She is very front-paw able - the dog pokes me in the leg to get attention, for example- and while I’ve seen her use both left and right paws, she definitely shows a preference for her left.
So… do dogs have handedness?
Yes, according to Every Little Thing
https://gimletmedia.com/shows/every-little-thing/49hrr64/is-your-pet-a-righty-or-a-lefty
Don’t know, but that is one good looking dog.
Dogs certainly can display “handedness” but they are more evenly distributed between lefties and righties and are also more likely to have no preference. SOURCE
Thanks! Luna is beautiful and smart as a whip. And she looks a lot better than when we got her from the shelter.
I once read an article about trilobites being right handed. Apparently, it’s common to find fossils where they have a scar from something biting them, and the scar was on the same side most of the time, and the speculation was the trilobite was ring to escape, and turned to the side, and usually turned the same way.
So I’d guess that dogs are handed.
Based on the replies here, the answer seems to be “yes”, which surprises me. My experience with my Bernese Mountain Dog was that he was mainly adept at using his snout rather than paws. For instance when he wanted to go out or come in, and only the screen door was closed, he’d slide it open with a quick motion of his snout. He could easily have done it with his paw but the snout action was more natural to him. (And the silly dog never closed it behind him, either!) The only time I recall him using his paws for a utilitarian purpose was to hold down a beef bone he was gnawing on, and he seemed to use whichever paw was most convenient at the time.
BTW, @JohnT, Luna is one beautiful dog. Love those eyes! 
As mentioned above not all dogs display a paw preference (they tend to but it is not uncommon at all for them not to as well). Yours may well be one of them.
My last dog was definitely leftie (for instance, anytime you would ask her to shake 99% of the time she’d offer her left paw to you).