With the new Integrationsgesetz, which is valid since Aug. 6 2016 there is the so called Wohnsitzauflage.
It means that you are obliged to stay at least in the federal country, in your case NRW after you received your Aufenthaltstitel.
You can even be bind to stay in the city/ commune where you received your Aufenthaltstitel.
Good news is, that you can freely choose your residence if you manage to get a job with at least 15h per week and an income of 712€.
I am not sure, if you nevertheless have to bring in an application for moving your residence in the town you currently live in.
So I would not recommend in any case to change your residence without informing your local authorities in advance or make an formal request in order to avoid any penalty.
I would recommend to make an appointment at your local asylum department and ask for advice how to proceed:
More help assistance and consultation you can receive in Dortmund from
APP who want to help refugees to integrate into the labour market:
or the Flüchtlingsrat nrw where I found a lot of info concerning the Integrationsgesetz: