Renters insurance, as the name implies, is focused on providing coverage for the renter. It does not cover any property damage, as the owner/landlord is responsible for their own insurance to cover those costs.
Therefore, roof leaking is not covered by renters' insurance. However, any of your personal items that are damaged by the roof leak would be covered by your renters' insurance policy.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.