One of the places the City uses to post the positions open within City Government and City Government offices in on this webpage http://hhoh.org/city-employment.html
If you don't see a current opening for a position you can still use the contact information to inquire about how unadvertised positions are filled and to get general information about how often position become available and how the public is notified.
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City's Job Opportunity Page
If you don't see a current opening for a position you can still use the contact information to inquire about how unadvertised positions are filled and to get general information about how often position become available and how the public is notified.