Can you be suspended without pay for non-investigative purposes?

Probably.  Do you have an employment or union contract that provides otherwise?  Is there a company policy to the contrary?  Has this action stemmed from some form of discriminatory workplace practice (ie due to race, religion, age, gender, etc).  If not then you can be suspended for any reason or no reason at all.  The reason is that most employment relationships are "at will" employment.  So unless 1 of the 3 exceptions above applies to your situation, your employer is free to do as it likes.  Of courese, your free to work for there or not.