Whether or not you are liable for income tax is determined by your place of residence or habitual abode, not by your citizenship.
For example, if you moved to Germany permanently, your place of residence is in Germany and you will be subject to unlimited income tax liability. The same applies if you stay longer than six months in Germany and thus have your habitual abode here.
Unlimited income tax liability means that both income earned within and outside Germany will be subject to taxation in Germany. Therefore, you may be obliged to submit an income tax return. By contrast, persons earning income in Germany but having neither their place of residence nor their habitual abode in Germany are subject to limited income tax liability.