Could an employer require only some hourly employees to punch a time clock, but not others? (local municipality)

In order for me to evaluate whether something were legally amiss, I would have to hear the reasons the particular work group has been singled out for different treatment.

Maxwell Taylor is correct. The mere fact that one hourly work group is required to punch a time clock while most of the hourly work force does not have to is not, by itself, a legal violation if the employer has a legitimate, non-discriminatory reason for requiring this (for example, if punctuality was particularly important for that work group). Legal violations would arise if the employer required this for a discriminatory reason. So without more information, it's impossible to say.