May have found the answer to my question, but this is a recent change as it did not apply to Colorado in 2013, 2014 or 2015.
1099-G Requires State EIN Information for Electronic Filing
For certain states, when marked for electronic filing, the 1099-G Wks will require additional payer information such as EIN and address.
These states, when marked for electronic filing in the return, will trigger errors for additional information on the 1099-G:
It has also been noted that when one of these states is included in the return, other states (NY, NJ, etc.) may require entry as well.
Intuit does not keep a list of the EINs associated with each state. Please contact the state directly to acquire this information.