Hi Lakshman P,
Could you please share the detailed error message about your failed test? It can help us find out what happened with your test.
According to below thread, there has some configuration need to set for parallel. Please refer to this thread to check whether your problem is caused by the settings.
http://stackoverflow.com/questions/3917060/how-to-run-unit-tests-mstest-in-parallel
And if possible, please provide more detailed information about your test, such as code snippet, settings, to help us reproduce your problem.
Best Regards,
Weiwei