Short Answer is: It depends! And without more facts as to the reason, license of the "dance studio", is it public or private, the purpose of the wine serving, etc, it is hard to provide you with a more definitive answer, and you really need to do some additional research and/or state your precise concern to get a better assessment of the legal issues involved. I truly wish you the best of luck!
If you want to serve alcohol at an event or venue where a member of the public can attend a California Alcohol license is required. Giving, selling, or furnishing free alcoholic beverages without a license is illegal under California Business & Professions Code Section 23300. Businesses that engage in such activity will be considered illegal bottle clubs if alcohol is provided to, or consumed by, customers California Business & Professions Code Section 25604. Even if you are having a private party at your studio and the alcohol is being given without charge to guests of the party, if it occurs at a retail business, the Department of Alcoholic Beverage Control will assume a violation.
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This is a very good question and comes up in my practice often with restaurant operators. My best recommendation is to call the California Department of Alcohol Beverage Control. They are very helpful and can answer your questions specifically. They also have a website that is helpful too.