Coolant is the fluid nobody checks until the temperature gauge moves. For a car under a service contract, that gap in attention can also become a gap in the paper trail. The check itself is easy. The hard part is deciding who does it, so nobody assumes someone else did.
Who looks at the reservoir
Name the person. Many owners check the coolant reservoir during a routine look under the hood, and a shop checks it during a visit, but a visit is not a schedule. Write down the owner's name, or the name of whoever drives the car most, next to the check. If two people share the car, decide which one reads the level and which one tops it up, so the job is not split in a way that leaves it undone.
How to check it without making it worse
Look at the reservoir when the engine is cool, and read the level against the marks on the side of the tank. Never open the pressure cap on a hot system. Use the coolant type the owner's manual names, because mixing types is a question for a shop, not a reason to guess. Top up only to the marked range. A level that keeps dropping is a symptom to bring to a shop, not a reason to keep adding fluid.
Ask about the contract before the next service
Read the maintenance clause in the contract and find out what it requires. Ask whether a coolant service must be done at a particular kind of shop, whether a self-done top-up needs to be recorded in a particular way, and what proof the provider accepts that the work was done. The answers differ by contract, so take them from the form and from the provider in writing rather than from a verbal reassurance at the counter.