Although managed code implies no direct memory management, you still have to manage your instances. Those instances 'claim' memory. And it is all about the usage of these instances, keeping them alive when you don't expect them to be.
Just one of many examples: wrong usage of disposable classes can result in a lot of instances claiming memory. For a windows service, a slow but steady increase of instances can eventually result in to much memory usage.
Yes, there is a tool to analyze memory leaks. It just isn't free. However you might be able to identify your problem within the 7 day trial.
I would suggest to take a loot at the .NET Memory Profiler.
It is great to analyze memory leaks during development. It uses the concept of snapshots to compare new instances, disposed instances etc. This is a great help to understand how your service uses its memory. You can then dig deeper into why new instances get created or are kept alive.
Yes, you can test to confirm whether memory leaks are introduced.
However, just out-of-the box this will not be very useful. This is because no one can anticipate what will happen during runtime. The tool can analyze your app for common issues, but this is not guaranteed.
However, you can use this tool to integrate memory consumption into your unit test framework like NUnit
or MSTest
.