BBB is absolutely worthless. If you are a paying member they will keep your record clean. They don't even check up on the information a business provides them with!
Consumer Affairs is a government agency and keeps the best records on companies. They are unbiased and accurate. Definately check with Consumer Affairs.
Also, consider doing a general internet search on the company to see what, if anything, you come up with on them.
I agree with Drew - the BBB is worthless. I can't tell you how many people who've gotten scammed by companies who say they checked with the BBB first. (I investigate and/or prosecute companies and people that scam the public out of money, generally speaking.)
What kind of company is it and what are you looking at it for? Different state agencies keep records on companies for different purposes. It helps to know what the business does.