There is no standard checklist for knowing what all statutory certificates a vessel is required to possess. But each company usually develop this checklist and provide this to the vessel.
This checklist could be in form of a PMS software that alert the ship and shore staff of the certificates / Surveys that are coming due in near future.
Apart from that "class survey status" lists all the statutory certificates of the ship.
Class status report also shows the validity of each certificate alongwith due date of the surveys related to each certificate.