You can submit a request through the city of Sacramento.org website. Someone will get back to you within five business days. No guarantees you'll get a reservation but you can give it a shot.
There are no reservations for the few picnic tables; first come first serve. If you are not able to snag some of the tables, there is a large grass area that you can use for a party - set up a shade tent with tables and chairs + decorations and BAM! You got a good time ready to happen! I would still call them to make sure you're good to bring in all the party supplies.
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