The US government did a study on highway safety impacts from radar detectors in 1988[1]. While they were able to determine that the presence of a radar detector increased aberrant braking, none of that aberrant braking caused a collision or seemed to be inherently unsafe to other drivers, and also the amount it was observed was statistically very low. They weren't able to determine what the effect was on if a radar detector resulted in more speeding because that was too complex to study though.
[1] https://rosap.ntl.bts.gov/view/dot/1481/dot_1481_DS1.pdf