It is normal to leave your log book with your flying school.
It might be normal practice around the flying schools but that does not automatically mean it is a legal requirement. The log book is a personal record of your flying experience and is a legal document. You are entirely responsible for its accuracy/true statements etc. It does not "belong" to the flying school at all. If the flying school management wish to check your record keeping is valid, then all they have to do is to ask you to present your log book for verification and then hand it back to you. That is a personal viewpoint based upon absence of anything specifically to the contrary, documented in the Regulations or Orders.