I moved in May from Washington state to Arizona.How do I file state taxes? Washington doesn't have income tax, do I pay income tax to Arizona for my income in Washington?

No. You are a part year resident for each state. You only pay tax to AZ for income after the date of the move. Make sure you set up the part year in Personal Info correctly.

If you were a resident of 2 different states during the tax year (for example, if you moved from one state to another), you'll normally file part-year returns in both states, assuming each state collects income tax and you had income in each state.

TurboTax handles part-year returns, but you need to make sure you've set up your personal information correctly to trigger the part-year state interviews:

1. With your return open, select Personal Info.
2. Click Edit next to your name.
3. Select your resident state from the State of Residence drop-down.
4. Answer Yes at the line below (that you lived in another state during 2017).
5. Select your former state from the Previous state of residence drop-down.

1. Enter the date you became a resident of your new state. This can be the date you arrived in that state.
2. Select Continue to return to the Your Personal Info Summary screen.

1. Repeat Steps 3-5 for your spouse, if needed.

After you finish your federal return, you'll automatically move to State Taxes, where you'll see your part-year states listed. We suggest you prepare the return for the state you currently live in, followed by your former state. 

Important: If you also see a nonresident state return on the State Taxes tab, complete that return before you work on your part-year return(s) to ensure your tax credits are calculated correctly.

Washington state doesn't have an income tax. What happens in that case?

Nothing, except that you have to show that you moved to AZ from somewhere. Don't fill out a WA state return.

I believe it isn't working for me. Both Federal Tax and AZ state tax are being calculated almost at the same amount. Less than 5% apart. When my income in seattle accounted for about 30% of my annual income

Delete AZ. Make sure everything is set up as above in Personal Info. Make sure that your W-2s have the states info apportioning income. Re-enter AZ. It does work.

My W2 from seattle don't have state. Should I add state to box 15 through 18?

It would be a good idea, but the program will need a state ID to efile. You may not be able to get one since there is not state income tax. You could try to call your DOR
<a rel="nofollow" target="_blank" href="https://dor.wa.gov/">https://dor.wa.gov/</a>

Do I file as Form 140PY - Part-Year Resident or Form 140 - Resident? how does that work?

Part year. https://azdor.gov/individual-income-tax-filing-assistance/determining-filing-status-non-residents-part-year-residents

You also have to file a non-resident return in CO.  Rental income from a property located in CO is taxable by CO.  The portion of your rental income that you received after moving to AZ is also taxable by AZ, but you'll be able to take a credit on your AZ return for the tax paid to CO.  Be sure to complete the non-resident state return BEFORE you do your home state return, so that you'll get the proper credit.

I have a similar situation except no property.  I owned my own business in WA state and worked as a contractor until the end of June when I moved to AZ.   Started a job in October in AZ, I have no idea how to file taxes.