Instructions
Search lists of basketball players for the person's name. The Official NBA Basketball Encyclopedia lists every player who ever played in the league. Most colleges have a media guide with an all-time player list, which is often accessible on the school's website. If not, call the college's sports information department and they should help you.
Contact sports cards magazines and autograph publications. Those outlets have experts who could often figure out the signature. They may even write about it.
Use what the autograph is written on as a clue. If it's on a game-day program, ticket stub or yearbook, then it won't be hard to narrow your search. Sometimes people meet someone in a restaurant and get an autograph on the back of a menu. Find out what city the restaurant is in and note things on the menu like who the owner is or dishes served. If the restaurant no longer exists, contact the city historian. Based on those clues, you might be able to identify the year and location. Then, check the area teams and players for that time frame.
Contact the Naismith Memorial Basketball Hall of Fame in Springfield, Massachusetts, and the National Collegiate Basketball Hall of Fame in Kansas City, Missouri. The museums display basketball memorabilia and would know how to identify autographs.