It is common for the City to require notice of any other job you work at to make sure there are no possible conflicts of interest, and to make sure your duties at that second job do not affect your ability to do your job at the City. But I have not heard of a blanket denial against any other work at all. The reason they gave you that they are paying you on vacation so they can control you does not make sense to me. You should speak to an attorney who is familiar with the law in your state on these issues of public employment rights
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