If I download Turbo Tax premier, does it come with state income tax filing??

The download Premier version includes one state download in the price. Efiling of the state return is additional but you can print and mail it without paying additional. 

If you use the CD/download then yes, there is a state software program included for ONE specific state which can be used to prepare returns for that one state.   The CD/download lets you e-file up to five federal returns for free but there is a fee to E-FILE s state return---you can avoid the state e-file fee by printing and mailing the state.

If you use online Premier you pay separately for federal and state returns.

Your question is posting from online Premier.

Use this link to buy the CD/download version from TurboTax or you can by it from outside vendors such as Amazon, etc. If you buy it from outside vendors make sure it includes the state download if you need it. Some states don't have state income tax so in the past some vendors offered products without the state being included in the price. 

https://turbotax.intuit.com/personal-taxes/cd-download/