I live in two states. What is the proper way to be a dual resident?

I don't think this is an immigration question.

Is there an immigration question?

Consult with Certified Accountant (CPA) and/or a tax attorney. Research to see which state is less of a tax burden on your wallet, and choose to make that one your place of primary residence. It doesn't hurt to have 2 drivers licenses issued by 2 different states, if you can manage it. Register your cars in the state that charges less for car registrations. For instance, many people living in CA still carry OREGON or Arizona or Texas plates simply because it costs much less to register cars in those states as opposed to CA. In your case it might even be legal do do so.