have a skeleton in the cupboard / in the closet - mít kostlivce ve skříni (= mít tajemství)
1. Do you have a skeleton in the cupboard that you are desperately trying to keep hidden? What guilty burden are you carrying from the past? (Google)
2. Andrew Laurence: "Most of us have a skeleton in the cupboard." "Yes," I said, "but a gun is easier to conceal." (Google)
3. The many people I have contacted and spoken to in the course of researching and writing my book have convinced me that the old adage is true – every family does have a skeleton in the cupboard. (Google)