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.
https://accountants-community.intuit.com/articles/1610781-1099-g-requires-state-ein-information-for-electronic-filing
1099-G Requires State EIN Information for Electronic Filing
Description
For certain states, when marked for electronic filing, the 1099-G Wks will require additional payer information such as EIN and address.
Solutions Description
These states, when marked for electronic filing in the return, will trigger errors for additional information on the 1099-G:
Arizona
Colorado
Connecticut
Georgia
Illinois
Indiana
Minnesota
North Dakota
Oregon
Utah
Virginia
West Virginia
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.