The phrase refers to making a phone call. In early detective novels, it's a fairly literal reference to someone "dropping a dime" into a payphone slot to make a call (typically, to the police to rat out or snitch on some criminal activity).
Similarly, it is asked, why do they call it a dime in basketball?
When payphones were most popular (long before cell phones were the norm) it cost a dime to make a phone call. In this sense, “dropping a dime” or giving someone a dime was assisting someone to make a phone call. Most people believe this phrase ended up transferring over to the NBA as helping a teammate make a basket.
What is dropping a dime in basketball?
A “dime” in basketball is the same thing as an assist. For those unfamiliar, a basketball assist occurs when one player makes a pass to a teammate which leads that teammate to score a basket. Assists are an important statistic kept for basketball players during each game.
Where does the phrase drop of a dime come from?
"At the drop of a dime" sure sounds like a mixture of "at the drop of a hat" with "to drop a dime on" (to snitch on). The phrase comes from the old cost of a telephone call (ten cents) by which a criminal could rat out his former friends.