I have a book that is entitled Those Good Old Golden Rural Days. The Rural Schools of Franklin, County, Nebraska 1875-1995. This book was published in 1995. This book was put together by the Franklin Senior High School Students with Teacher Les Sidlo and his Information Management Class that put this book together.
Woody School was District #71. It was open from 1900 until 1951. It was located about a mile north of the Kansas/ Nebraska State line in Turkey Creek Township and section #35. Southeast of Naponee and Southwest of Bloomington
I hope this helps