All I know is it starts with a little girl who pushes which I think another girl into traffic which the guys sees and think this little girl tries to go after him.

Aw man, I know this one by description but not name! Let me help you out here:

The girl is constantly playing on a gameboy and the guy who witnessed it is freaked out because he saw her save her game before she pretended to be concerned for her friend.

Later the girl somehow is able to tie up the MC and hide her in her closet while her mom or some other relative is home. She then starts to torture him. I dropped it because of the fact that he fell victim to a child but if I find the title I will report back here.

Shoujo Fujuubun?

This is it!