Collecting A Reward for Crime Tips

How does this work? I usually see things like “Police are offering $25,000 for information leading to the arrest of John Doe.”

First of all what does “information leading to,” mean? I mean, the cops could use your information and deny it lead to the arrest. So how does one collect?

Another thing is does one have a legal responsiblity to report crime?

Let’s use an exaggerated example:

I am walking down the street talking on my cellphone when I see a robbery, I duck in the bushes and capture a mini-movie on my cellphone.

Now is there a law saying I have to go to the cops with said information?

If not what if I thought to myself “Hey you know what, I’ll just keep this until the police have no leads and offer a reward.”

Then let’s say two days later the cops offer a reward and I come forward. I’m sure the cops will ask “Why didn’t you come forward sooner.” Of course you can always claim you were scared.

So in general how does the reward work. I am talking about rewards offered by government like the police or FBI, not the private ones, such as the Ramseys offered when JonBenet got killed.