Do I need a specific binding for park skis?

You don't need a park-specific binding, but certain features are beneficial. Look for bindings with durable construction that can withstand hard landings, a reasonable DIN range for your ability (most park riders need 8-14 DIN range), and a solid, direct connection to the ski. Some bindings are marketed as freestyle-specific with features like wider platforms or elastic travel for retained releases on off-axis landings. Any quality alpine binding mounted on a flat alpine-compatible park ski will work.