Keeping a bool around that indicates that the mutex is owned is a grave mistake. You are not making the bool thread-safe. You got into this pickle because you are using the wrong synchronization object. A mutex has thread-affinity, the owner of a mutex is a thread. The thread that acquired it must also be the one that calls ReleaseMutex(). Which is why your code bombs.
You in all likelihood need an event here, use AutoResetEvent. Create it in the main thread, call Set() in the worker, WaitOne() in the main thread to wait for the worker to complete its job. And dispose it afterwards. Also note that using a thread to perform a job and having your main thread wait for its completion is not productive. You might as well have the main thread do the job.
If you are actually doing this to protect access to an object that’s not thread-safe (it isn’t clear) then use the lock statement.