It all comes down to how comfortable you feel using right or left handed clubs. Generally those who write right handed are right handed golfers and those who write left handed are left handed golfers, but there are exceptions Phil Mickelson writes right handed, and many right handed golfers are left handed.
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Your dominant eye and hand plays a part in this. Normally the hand you bowl with or any similar activity, is the hand you'd pull your bow back with. It's also important to be aware of which eye is dominant. Most cases this will be the same side, if not, go to a bow shop and they will work with you.
Archery is like shooting firearms . . . you find out if you are right-eyed or left-eyed.
Get a helper and face them from 8 or 10 feet away. Then hold up your finger with your thumb and index finger making an "O" shape. Look at them through the "O".
Whichever eye they see through your "O" is your dominant eye, and is the one you should aim with, no matter whether you are left-handed or right-handed.
You would use the hand you write with usually but if you want to get technical you would hold the bow with the same hand as your dominant eye.