After Riley v California (2014), a warrant is required before the search of a mobile device. Therefore, in a scenario where you are asked to unlock your device, the only question is whether you are required to cooperate by giving your password or offering your finger. In the case of a password, the answer appears to be no, due to the privilege against self-incrimination. In the case of fingerprints, there is no such right. You are merely identifying yourself to the phone and your identity cannot be construed as incriminating testimony.

http://www.supremecourt.gov/opinions/13pdf/13-132_8l9c.pdf

http://scholarlycommons.law.northwestern.edu/cgi/viewcontent...