Your whereabouts can more or less accurately be determined by, for example, your signal strength relative to the cellular base stations in your vicinity. The further away from civilization you go, the harder it will be, but that's inversely proportionate to your coverage which kinda defeats the purpose. More importantly though, records of your location will be kept - so even if you disable your phone, your last recorded location will be known for some amount of time. I would not bring my phone with the intention of using it within minutes of a place where I don't want to be found. That said, since this involves the police I wouldn't expect things to move very fast unless maybe you're a most wanted criminal.