Personal Radiation Detectors (PRDs) should not be used as a standalone law enforcement mechanism.
Common items--bananas, spinach, peanuts, brazil nuts, pottery, kitty litter, patients with recent radiation treatment for cancer--emit gamma radiation that will cause false positives in PRDs. As an example, the Port of Long Beach has over 250 false positives per day.
PRDs as a standalone radiation detection mechanism for law enforcement purposes is probably a poor strategy due to these excessive numbers of false positive readings from such innocuous sources, an inability to detect beta radiation, and unreliability in detecting heavily shielded sources. PRDs, as I understand it, are meant to be used in conjunction with other radiation detection technology (e.g., imaging systems and spectrographic monitors) in a "layered" defense.
Thus, stopping or searching a person based solely on a PRD positive reading, in my opinion, would be unwarranted (and probably a violation of his or her Fourth Amendment rights--although, of course, this is for the courts to decide).
[Note that I called detection of radiation from bananas, kitty litter, etc. by PRDs "false positives" above. These are false positives (Type I errors) only in the sense that PRDs are functionally devices to look for "bad stuff," and they identify "bad stuff" a lot more than it is actually present. Note, however, that these detectors are largely correct in identifying gammas sources. (Their actual false positive rates (i.e., an indication of detection of gamma radiation when there is no source) is more like 1 or 2 percent)).]