When you move to a new state, you become a legal resident on the day you begin living in your new domicile - your "permanent" home (whether owned or rented) - there. (Temporary lodging such as a hotel room doesn't count.) Until that day, you remain for tax purposes a resident of the old state.
The date on your new drivers license, voters registration, etc., is irrelevant. That's because people sometimes move to a new state and don't get their drivers license or voters registration for months or even years. The date that counts is the date you establish your "domicile" - your permanent home - in the new state.
If you move in 2018, you'll be filing a part-year resident return in each of the two states. This FAQ explains how to do that in TurboTax: https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
After you move to CO your rental income from your SC properties will still be taxable by SC, as well as by CO. But you'll be able to take a credit on your CO return for any income that's taxed by both states, so you won't be double-taxed. (You'll take a credit on the CO return for the SC taxes you pay after becoming a CO resident.)
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
