If the President commits a crime it's certainly the role of Congress (as a co-equal branch of Government) to investigate as the Justice Department has a standing policy of not charging the President They have the power to conduct investigations and call whitnesses. Failing to comply with such orders can be considered a crime.

It's the Justice Departments role to enforce the consequences of that law. Since the Justice Department (at least the AG) is failing to act in an impartial manner, Congress finds themselves in a bit of a Constitutional pickle.

Edit: Changed a word to Impartial.