In states where drug testing is not restricted, nothing prohibits a drug test. However, in states that do not allow suspicion-less drug testing (such as random tests), it could be problematic to test on the basis of reasonable suspicion if no signs of drug use are currently present. The arrest happened while off work, and there is no evidence that his work performance has been impacted.
The best response, at least initially, it to simply watch work performance more closely. If any signs or symptoms of drug use are detected, as with anyone, proceed with reasonable suspicion drug testing.