'balls have dropped' what does it mean?
Solution 1:
It means someone who has started puberty. In your context, they'd like to arrest someone who isn't a child - they'd like to arrest an adult or teenager.
From RespectYourself.info
People often use the phrase a guy’s balls drop to imply he has started puberty. What this means is that a his scrotum, the wrinkly sack just behind the penis which holds his testicles, starts to hang a bit lower, away from his body. Technically a boy’s testicles should have dropped during infancy, they literally descend into the scrotum; if this doesn’t happen by the time he is five he will have to have an operation. However, the term – balls-dropped has always been misused to mean a lad has started to produce sperm during puberty.
Solution 2:
I want to add to the current top answer, to contrast it with a different but similar expression "the ball has been dropped". I'm adding this here because someone else might come across your answer when it is this other expression that they are encountering.
This comes from the metaphor of juggling balls. which means something completely different and is not even vulgar as is even part of acceptable corporate office-speak. It means that something that needed constant attention/maintenance was neglected and it is ruined.
The key to distinguishing between the phrases is "ball" versus "ball s". In the plural it almost always means testicles (and is crude) in the singular it refers to this other phrase. A notable exception being "Having multiple balls in the air" it a counterpart to this expression (ie "the ball has been dropped", in this can meaning that there are multiple things and none of them have been yet "dropped") and not testicles.
Once again, this is a SIMILAR expression but DIFFERENT from the one you have asked about.
Solution 3:
Similar to ArtB, who mentioned that "the ball was dropped" (or "he dropped the ball") has an altogether different meaning from the expression "his balls dropped", I wanted to chime in with yet another expression, and that is the expression "the ball drop". Again, I'm only adding this in case Google searches have cause for confusion on the semantics. "The ball drop" is actually a tradition that is celebrated every New Year's Eve that occurs at 11:59pm in New York Times Square as an internationally televised annual event, where during the final seconds of the year a large ball erected on a tower is pulled down over the course of about 10 seconds. When it reaches the tower base, the time is 12:00am of the next year, which is when the fireworks go off, confetti is thrown, the music plays, and people kiss. And it's about to happen again in about a month as of this post. :)