I lived in NY for 3mths and Colorado for 9 months in 2023. For taxable income, it keeps using the sum of both?

If in 2023 you lived in NY and CO, you need to file Part-year resident returns for NY and CO and allocate your income between the two states. 

You need to make sure you've set up your personal information correctly in TurboTax .

To do that please check: How do I file a part-year state return?

To allocate your wages, select the earned income from the link below and follow the instructions. 

Also, any unearned income  such as interest, dividends, capital gains, social security, and IRA distributions is taxable in the state you were living in when you received it. 

How do I allocate (split) income for a part-year state return?

On CO return, Income tax is prorated so that it is calculated only on income received in Colorado or from sources within Colorado.

NY calculates what your New York tax would have been if you earned everything in NY, but then prorate that tax based on how much of your income was earned while a NY resident.

 For more information, check: 

ny.gov

co.gov