1960's slang. Calls from a payphone used to be ten cents - a dime. "To place a telephone call; (specif.) to inform on someone by making a phone call to police." -- "Random House Historical Dictionary of American Slang, Volume 1, A-G" by J.E. Lighter, Random House, New York, 1994.
Informing or letting information leak out. "Out to get rich, but I'm no *****, no need to drop a dime" -- Dayton Family (What's On My Mind II) . If a snitch drop dime on my crimes I'ma have to park at Rally, Run up and spark his family -- Pacewon (Sunroof Top) .
Sometimes used in a "double-meaning" punchline. I dropped a few nickels but I don't drop dimes. -- Andre Nickatina (Bay Area 415)
'Dropping a Dime': means making assists on the basketball court, (dropping dimes). Iverson be dropping dimes about 9 to 10 times a night. Did you see that dunkadelic reverse slam on Shaq, AI was dropping dimes to Webber all night long.