Yes a catering business can be started from home however you need to contact your local municipality and the health department in order to get the proper licenses to operate the catering business.
Also you'll need to make sure that you can actually operate a business of any type out of your home before you actually start the catering business.
The health department will need to check your home over and be sure that you're cooking the food properly and keeping the house and kitchen and utensils clean.
Then you'll have periodic inspections from the health department since your business involves food and you must follow strict guidelines when operating any type of food business including the catering business.
Personally I would rather just open up a commercial location if possible to start the catering business to keep thing separate and not have the health department come to my house.