Why would you need to use a constructor in your test classes?
I use [SetUp] and [TearDown] marked methods for code to be executed before and after each test, and similarly [TestFixtureSetUp] and [TestFixtureTearDown] marked methods for code to be executed only once before and after all test in the fixture have been run.
I guess you could probably substitute the [TestFixtureSetUp] for a constructor (although I haven’t tried), but this only seems to break from the clear convention that the marked methods provide.