Did you ask your brother why he has stolen the photocopy from you?
How old is your brother?
Is he married? If yes, How good is your SIL?
Has he stolen it for fun or to create trouble for you?
What are his intention and explanation?
Let us know for further discussion on the subject.
No life without Sun
This often being the case that even the duplicates or the photo copy of the original can still be used for some illegal activities & therefore utmost care needs to be taken in order to make those secured too so that your personal data also may not get stolen or used for something which you are not informed of or to agreed upon.
In this case the document is only a photocopy and not the original so there is nothing to worry.
You must ask your brother for this irresponsible act. He has done it on his own or someone has instigated him to do it. He should also be warned not to do such things in future and tell him that if he does such things then nothing will be kept in his access and he will become a stranger in his own house.
Knowledge is power.
Don't feel bad with my narration as to how the photocopy could create trouble for you. It is only my imagination of a bad situation.
Presume your brother is an ill minded person and not loved by you. He wants to trouble and fix you. He involves in a crime. He leaves your photocopy of the license at the place of crime. The criminal case is being investigated. Your photocopy is found as a clue to trace the culprit. The investigating authorities reach you to question you.
Now you can imagine what would be the next. Anyway, you will overcome.
So, it is better to lodge a complaint with the police, if you feel that your brother might create a problem for you.
No life without Sun
But you should inquire why has he stolen the photocopy of the driving licence as it's of no use for him unless and until he using it as a proof for buying something or for applying something on your name. But everywhere they ask for the self-arrested document but still, he may do the fake sign of yours on the document. So you should be careful from him and should inquire about the same.
" It is better to be hated for what you are than to be loved for what you are not" ... Andre Gide
Beware! I question everything and everybody.
I had a practice. If I give a xerox copy to anybody I will write on that to whom I have given and what for I have given and sign on that. In that case, they can't use that copy for any other purpose. I will put the date also on that so that when we have given that also is known. If we take sufficient care, I think we will have peace of mind. Anyhow be careful with your original papers and don't keep them in such a way that somebody else can easily approach for those papers. Please talk to your brother and see that he will not be using it for any unwanted purpose.