Amending your federal tax return over an error in local taxes is unnecessary, unless the change in local taxes affects your itemized deduction for state and local taxes.
The IRS will only follow-up on corrected W-2s if the changes affect your federal tax.
You might want to go through the "amend a return" process to update/amend your state return, since that is often where your local tax return information is reported. Depending on what changes were made to your W-2, there may be a need to amend your state return
See How do I amend my 2020 return?
