Months after a New Canaan Country School neighbor sued the Planning & Zoning Commission over its approval of a new athletic facility, the school purchased that neighbor’s property for $3 million, tax records show. New Canaan Country School has acquired the 8.3-acre property at 579 Frogtown Road, according to a property transfer recorded June 10 in the Town Clerk’s office. It’s located in the two-acre zone. On June 4, the private school applied for a permit to construct the new two-story, 48,000-square-foot facility, which will include basketball and squash courts and will cost about $10 million to build, according to a building permit application. Newtown-based Claris Construction will be the contractor on the job, the application said.