Anyone who has had a cat urinate on carpet can attest that cat urine is a strong, noxious odor that is hard to remove. When a cat urinates somewhere other than the litter box, the cat may be sick or may be acting out and marking its territory. Regardless of what the circumstances are, if your cat urinates on an air vent in your house, you must address the situation immediately as the moment the heat or air conditioning flows through that vent your entire house will reek of cat urine.
Turn off the air conditioning or heat if not already off. Unscrew the air vent and remove it. Take a thick layer of eight paper towels and wrap them around the end of a broomstick. Hold them in place by wrapping a rubber band around the broomstick.
Insert the broomstick down into the air vent as far as it will go and mop up the cat urine. Add more paper towel if necessary to mop up the entire mess. Sprinkle a tablespoon of baking soda down the air vent.
Mix 3/4 cup of three percent hydrogen peroxide with 1 tsp. of dishwashing liquid in a spray bottle. Spray it down the air vent until half the bottle is empty. Allow all these ingredients to sit for two to three hours. After this amount of time smell the area again and repeat with more baking soda and hydrogen peroxide plus detergent mixture if necessary.
Remove the old paper towels from the broomstick. Wrap the broomstick handle with another clean layer of eight or so paper towels held in place with rubber bands and mop up all the cleaning agents down your air vent. Remove those paper towels and add a new layer of eight paper towels dampened with cold water. Wrap a rubber band around them to hold them in place.
Wipe down the area with the damp paper towels. Give the area about an hour to air dry. Spray cat odor neutralizer down the vent. Place the vent cover back in place. Screw it in.