If the parking space was part of the original rental agreement, then only a 30-day written notice is needed to advise the tenant of a change in terms of the rental agreement. As for the rent control issues, you will need to consult with a housing law attorney in your community.
This is not a substitute for a consultation with a housing law attorney.
The landlord can take away a parking space in rent-controlled Los Angeles ONLY if he also reduces your rent to compensate you for the loss of the housing service. If the landlord does not also reduce your rent (by a reasonable amount), he is illegally raising your rent.
According to the Los Angeles Housing Department ("LAHD") Rent Adjustment Commission regulations, your rent should be reduced from $60.00 to $200.00 per month, depending on the "density" of your neighborhood, i.e., how hard it is to park there. I am adding a link to the regulations relating to reduction of services.
You should call the Los Angeles Housing Department and ask to speak to an investigator--the investigator will write to your landlord and advise him that he cannot take away the parking space without reducing the rent.
Important things to remember: 1. The fact that I answered a question that you asked me on line, doesn't make me your lawyer. 2. Opinions are like noses--everyone has one. I just happen to think my opinions are right, but check with another lawyer too.
I agree with most of the answers from the other 2 attorneys, but I believe that if the unit is under rent control, that they cannot take the parking space from you for any reason. If the space is assigned to someone else and you file a complaint with the local rent control board, they will either demand that you get the space back, or if that can't be done, then you should get a reduction in rent. Most jurisdictions do give between $50 and $200. I am mostly familar with SM rent control board, so that has been my experiences.
This is general legal advice intended for informational purposes only and does not create and attorney/client relationship. If you wish further advice, please contact an attorney of your own choosing or you may contact me for further advice and make other arrangements including retaining my services.