Do I need to file Schedule K-1 (Form 1065) for Georgia? If so, where do I enter this info in Turbotax?

If you have received a Georgia K-1 reporting some state-specific information, then you do need to include it as part of your Georgia tax return.  However, there is not a separate place to enter a K-1 as part of your state return like the entries for a K-1 on the Federal side.  

Instead, you will need to look at what is being reported on the K-1 and go through the Georgia return to find a corresponding entry.  If you cannot find an exact match, try to determine if it is an addition to the Georgia return (income) or a subtraction from the Georgia return (deduction) and enter it into one of those categories.  Be sure to click the Learn More links as you go through the Georgia return because they may give you additional useful information.

Here's my scenario: The "Distributive Share of Total Federal Income" is -$11036. The "Georgia Partner Summary" page of my Schedule K-1 states the following:

As AnnetteB6 said, you will enter the adjustments during the Schedule K-1 section of the Georgia state interview. If there are not separate boxes for additions and subtractions, enter the net amount.