It is a typical Spanish paperwork and beurocratic mess.

Basically, no you can't fit your own. It has to be fitted by a garage and a certificate completed and signed/stamped. You then need to take the vehicle, the certificate and the fitting instructions to the ITV centre where they will relieve you of some money, do a check and then add the towbar to the 'Ficha tecnica' of the vehicle.

If you fit it yourself or don't get it authorised then your vehicle will fail its ITV.

Best place to get it done - a franchise of the make of vehicle.