Sarasota County ordinances (section 90 is about parks) only says glass containers are prohibited. We only say that folks must be responsible. You can find the county ordinances at https://library.municode.com/fl/sarasota_county/codes/code_of_ordinances
I don't know officially, but the park is very open and i don't think there would be an issue. But probably not on the island.
I'm not sure...I didn't see any signs allowing or prohibiting alcohol. Sorry!
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