I contacted the Nashville Police Department and they said that they can take official fingerprints for use by the states and the FBI for background checks.
We need to go to: 200 James Robertson Pkwy at the Criminal Justice Center
They have "standard cards supplied by the FBI for fingerprint submissions that are used for regular background checks."
They said, "Yes, we can do it. The standard fee is $9 for the first set and $1 for each additional set of prints if needed. We are open Mon-Fri from 7AM to 6PM. Please make sure to bring the form with you."