She already answered before I got this posted, but I'll go ahead and post it anyway.
Q: Does the District have off-leash Dog areas?
A: The only parks that have dog off leash areas are: Shawnee Mission Park, Heritage Park, and a new area on the Kill Creek Streamway (95th St. entrance point). Each of these has an enclosed fenced area. Shawnee Mission Park and Heritage Park have a swimming area for dogs. Kill Creek Streamway has a creek, but the banks are too steep and the water is generally only a few inches deep. None of the other parks has an off leash area.
http://jcprd.com/park_admin/faq.cfm