For a perspective on a different jurisdiction, NSW, Australia, see http://www.findlaw.com.au/articles/4487/criminal-law-mens-rea-and-the-guilty-mind.aspx
Mens rea is a common law doctrine inherited from English law and applies to common law crimes. In NSW, most common law crimes are now dealt with by statute, most notably the Crimes Act 1900 although many other statutes also detail criminal offences. The state of the law here is:
In R v Wampfler, the justices in the New South Wales Court of Criminal Appeal, used the judgment from the High Court in He Kaw Teh v The Queen as a basis, stated that for the purpose of considering criminal intent, statutory offences fall into the following categories:
the obligation is on the prosecution to prove mens rea, which is the original obligation
offences in which mens rea is presumed to be present, unless, and until material is advanced by the defence of the existence of honest and reasonable belief that the conduct in question is not criminal, then it is the responsibility of the prosecution of negativing such a belief beyond reasonable doubt
the guilt of a person is established by the objective ingredients of the offence, and mens rea has no part in the committing of the offence.
So, in addition to the categories where mens rea is required to be proved by the prosecution and the category of strict liability, there is a third category where the actions allow the assumption of mens rea and the defence is obliged to overcome that assumption. Which crime falls into which category depends on the wording of the statute and precedents.
murder is a crime where mens rea needs to be proved by the prosecution,
drink driving is a crime where mens rea can be presumed by the prosecution but may be rebutted by the defence,
breach of work health and safety law is a strict liability offence - mens rea is irrelevant.