As a rule, there is no obligation to inform the tax office of a change of address.
If the same tax office is responsible for your new place of residence, the tax office will find out your new address at the latest when you submit your next income tax return, so that you do not have to inform the tax office separately. However, if you are still expecting a tax assessment notice or other communication from the tax office, it makes sense to inform the tax office of your new address. You can do this in writing or electronically via ELSTER do this.
If you move to the district of another tax office, you must submit your income tax return to the tax office responsible for your new place of residence. This tax office requests the previous tax documents from the tax office previously responsible for you.
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You can find your local tax office here: