The Santa Barbara County Civil index is searchable by case names or number and can be limited by date range. Dockets are not available. The government operated site describes the index characteristics:

The Online Public Index includes cases from 1975 for General Civil/Family/Probate, and from 1997 for Limited Civil cases. There is a very limited number of cases filed as far back as the 1920s included in the Public Index. If you need to find a case with a file date prior to 1975 or 1997 as previously mentioned, please request a search of paper indices.
NOTE: “Due to the unification of Superior and Municipal Court records, there may be more than one case number for an individual or company, we advise that you look at all cases for that individual.”