You are asking about Form W-4MN for Minnesota. That's not the same as federal Form W-4.
Yes, you should both enter 1 on line A of Section 1. You and your spouse are not each other's dependent.
(I assume that you are asking whether one of you is considered a dependent of the other. Your spouse can never be your dependent. There are situations where a married person could be claimed as a dependent by someone other than the spouse. Such situations are not very common. One situation where it sometimes comes up is with young newlyweds who are still dependents of their parents.)
