Possibly BANG, YOUR DEAD (UK 1954) with Jack Warner.
As a youngster in the fifties I remember seeing a black & white film with the following plot.
As a joke a young boy is fooled by an older boy (possibly his brother) into thinking that he has shot him, and he runs away before the other children can explain the joke.
Thereafter it all becomes hazy, I think the setting was a block of flats in London and that the boy runs off to the coast, but that may just be my memory playing tricks with me.
Does it ring a bell with anyone and can they come up with the title?
Possibly BANG, YOUR DEAD (UK 1954) with Jack Warner.