We have a condo House Rule stating that no campers, motor homes, boats, or trailers shall be permitted to be parked or stored at any time upon condo property. Is a KAYAK a BOAT? (It does not need a license, and does not need to be registered in FL.) and can the board tell you what you can and cannot have ON or IN your vehicle?
Most likely they can enforce the rule, but you would need a lawyer to review the condo docs to give a more definitive answer. Any visitor with a kayak would be a violation against the owner they are visiting.
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Residential Real Estate Lawyer
The answer to this question depends largely on the covenants and restrictions of the condo association. I would take a look at those to determine if this was an original covenant (rule). If not, the next question is whether the board has the power to drastically change the rules. That said, they probably DO have the ability to restrict storage of the kayak. Regardless of licenses, a kayak is probably considered a boat.