Do I belong to the labor relationship with the traffic police brigade of Dunhua Public Security Bureau?

You have a labor relationship with your institution, not with the Public Security Bureau. You are equivalent to signing a labor contract with a public institution and being sent to work in the Public Security Bureau. The public security bureau is the unit that conducts daily management and business guidance for you, and your labor relations are the institutions that sign labor contracts with you. Labor remuneration is also paid by the institution where your labor relations are located. The public security bureau can give you some subsidies or extra bonuses according to the actual situation. Of course, this is unnecessary, because it is not legal labor remuneration.