"Secure in their persons, houses, papers, and effects"

In Texas, at least, the police can't go searching on your phone without a warrant — at least not while it's sitting in the property room. As the majority opinion had it:

'The Fourth Amendment states that “[t]he right of the people to be secure in their persons, houses, papers, and effects against unreasonable searches and seizures shall not be violated.” The term “papers and effects” obviously carried a different connotation in the late eighteenth century than it does today. No longer are they stored only in desks, cabinets, satchels, and folders. Our most private information is now frequently stored in electronic devices such as computers, laptops, iPads, and cell phones, or in "the cloud" and accessible by those electronic devices. But the "central concern underlying the Fourth Amendment" has remained the same throughout the centuries; it is "the concern about giving police officers unbridled discretion to rummage at will among a person's private effects." This is a case about rummaging through a citizen's electronic private effects – a cell phone – without a warrant.'

Good. If there's probable cause, get a judge to okay it with a warrant. If there's not, keep your hands off.