Static methods aren’t inherently thread-safe. They’re treated no differently by the CLR than instance methods. The difference is that one should generally try to make them thread-safe. (I can’t think of any .NET BCL static methods which aren’t thread-safe.) Instance methods are often not thread-safe because the typical pattern is to create an object and use it repeatedly from one thread, and if it does have to be used from multiple threads, the co-ordination involved includes making sure that the object is used safely. In very many cases that’s more appropriate to do in the co-ordinating code than in the object itself. (Usually you want to make whole sequences of operations effectively atomic – something which can’t be done within the object.)
Your Timer class is most definitely not thread-safe: two threads can stomp on each other’s data with ease, and there’s nothing to stop a thread from using “stale” data when calculating the duration.
Use the Stopwatch class instead – that’s what it’s there for. Admittedly if you want to use one instance from multiple threads you’ll need to take the normal steps to ensure safety, but you’ll be in a much better position in general. Admittedly Stopwatch is far from perfect too – see this question and the comment below for more details – but it is at least what the type is designed for. (Who knows, it may be fixed some time…)