If you intend to use your weapon to defend yourself, then you need to know the laws of the jurisdiction you are in. Meaning, if you travel with your weapon from state to state or possibly even city to city, you need to be aware of any idiosyncrasies of when you are permitted to use deadly force. For example, with Ohio's recent change to adopt a Castle Doctrine, the rules have changed a bit. But surrounding states that recognize the permit are all different and you should not simply assume you can act as you would in Ohio.
As far as any statement to the police, consistent with the applicable laws, you should say something like, "Officer, I was in fear for my life and defended myself against this attacker/robber, etc. (This is where you have to know what your particular jurisdiction requires - for example, do you have a duty to retreat before using deadly force or must you allow a robber to run away rather than shoot or detain them). I will be happy to cooperate with you but I am not going to say anything more until I have had an opportunity to consult with counsel." Better to be detained overnight than to mistakenly say something that will cause more trouble down the road.
If the individual flees, there is nothing wrong with giving a description. In fact, you want him to be caught as soon as possible. What you want to avoid is any description of what occurred because even when justified, you won't be thinking clearly. The adrenaline combined with the impact of being involved in such an incident should not be underestimated.
Eric