Depends on what qualifies as API down. We have a number of options here.
1. If we have a Health page which gets invoked periodically then that BT can be used for Health Rule (HR) creation. If there are no calls ( BT metrics not reporting) then it can be a case that APIs are down.
2. We can also create HR on App Agent availability metrics. If availability is down then one of the case could be that the Process is down so Agent is not able to report metrics. But if API is up and for some reason Agent is not able to report any metrics it will lead to a false alarm.
3. If this is IIS hosted app then you will be using an AppPool to host this application which in turn will have a IIS Worker Process (w3wp) to serve the request. We can create HR on the following metric available at Metric Browser and see if the number of w3wps is equal to 0 which will mean w3wp is not running hence won't be able to serve requests
Application Infrastructure Performance|<Tier Name>|IIS|Application Pools|<AppPool Name>|Number of working processes
4. If this is IIS hosted app then you will be using an AppPool which means you can check the status of AppPool itself. You can import the relevant Perfmon Counter using following doc and then create HR on it