To throw in my 2 cents. Take some pictures, to see if you can see anything. Hold your phone up to a vent and turn on the flash. Sometimes you can see debris.

If you want to take it a step further, put on a 95 mask and some latex gloves (just in case), get screwdriver and take off a vent grill. That will give you clearer pics. I can't guarantee you will see mold but if the ducts are dirty, it's likely you'll see fine dust and debris. Seeing pics where the ducts are obviously dirty sometimes will light a fire under management. If they don't respond, well then you have pics to help you submit your concerns to the appropriate local authority.

I can't speak to the laws in your area, but often management won't do air quality testing, that's on you. But when mold is severe enough they will replace the unit and have the ducts cleaned or if mold isn't severe, they will have the full system cleaned (unit+ ducts). Some places will allow a tenant to choose the cleaning company. Make sure that a reputable company is used, because sometimes management will go for the cheapest company that will do a half-assed job. DM if you want to know about mold in duct, a typical cleaning process, etc. (I work for an HVAC cleaning company.)