A "police inquiry" refers to an investigation conducted by the police to gather information and evidence about a crime or incident. It is part of their efforts to solve the case and bring justice. Full definition
I was shocked to have become the subject of a seven month police inquiry. (politics.co.uk)
Craig Mackinlay was interviewed under caution as part of an ongoing police inquiry into whether the party overspent when they were up against Nigel Farage. (totalpolitics.com)
Like a Terry stop, the tolerable duration of police inquiries in the traffic - stop context is determined by the seizure's «mission» — to address the traffic violation that warranted the stop, Caballes, 543 U.S., at 407, and attend to related safety concerns, infra, at 6 - 7. (claytonrice.com)