Witness statements are what you receive when you witness an action that happens in the same city district as you.
You can receive them in your personals when you witness a Murder(wack), Theft(PickPocket) or an Assault(Mug). These are designed so that you can help (if you wish too) the person who was victim of the situation or their Family members.
Example 'wack' Witness Statement: You witnessed ropnejyam* WACK VictorClements
You may notice that the first name looks scrambled up, that's because it is. With witness statements the offenders name is scrambled so that it's harder for you to know who the offender was. Sometimes some characters of the offenders name are replaced with * making it even more difficult to know who the offender was. You are however able to unscramble the name using the 60 second online list at the bottom of the screen on MafiaReturns.