There has actually been a number of times when this has been an issue, and people who are both civilian police and Reserve soldiers have tried to do both at the same time. Suffice to say that legally it is one or the other - if in defence uniform an individual can have no civilian policing powers, and if off duty and out of defence uniform a Reservist has no powers under the defence act/DFDA.A big laugh is the number of Army Reserve MPs (and reservists in general) who or police members in civilian life. God help a transgressor who does something bad, or stupid enough to justify a cop to recall themselves to duty while on reserve service, the amount of paperwork would be phenomenal and ensure the officer concerned was already more than annoyed at the situation.
There was one funny incident a few years ago where a defence vehicle driven by soldiers was pulled over by a civilian police officer, who also showed them his defence ID (a reserve SNCO) and asked to see their military paperwork to authorise use of the vehicle. The driver told him to go f#*% himself as he wasn't on duty. The Reserve SNCO then tried to charge the soldiers (a military charge) for disobeying orders. The Reserve SNCO was very quickly and forcefully put back in his box by the chain of command, and told to stop being such a wanker.