Liquor licenses are usually under the control of the Alcohol Beverage Control (ABC) type state agency.Please check on the internet at Tennessee.gov for the published state regulations on obtaining a liquor license.I ,however would believe that any criminal conviction on the application would not help them,and I know that all applications to any state agency for any type of license will have a background investigation as a part of the approval process.
Liquor license are controlled by the State of TN, however a criminal back ground check will be done and and criminal violation can keep you from getting your license. A DUI in particular is a flag. While it may not prohibit you from getting the license there will be added steps.
Start with this link:
It may also depend on whether the DUIs were misd or felonys and whether they were convictions.