Warning: even more boring legal synopsis follows
Sparteye's leagleyed analysis is not necessarily applicable outside Michigan.

The common law position (which prevails, generally speaking, in the English speaking world except where modified by statute) is that if a victim of an assault expires more than a year and a day after the injury was inflicted, the perpetrator is not liable to be convicted of murder. An element of the crime is that the offender causes the death, and if the consequence is too remote (in time or other circumstance) from the act, the chain of causation is broken.

Sparteye's right: there isn't a statute of limitations for murder. But that, with respect, doesn't dispose of the issue. A statute of limitations would prohibit the prosecution from commencing legal proceedings after a certain date. The further question of whether the act and the consequence are so remote in time or circumstance as to sever the causal chain between them is a separate issue.

My bailiwick, the Northern Territory of Australia, has modified the common law by enacting a Criminal Code, but our Code doesn't adopt the common law year and a day provision with respect to murder. It is in fact sphinxically silent on the issue. Nevertheless, the old rule still seems to survive in practice, and is probably still good law here.

Although the Code generally displaces the common law, where it doesn't cover the field, the common law continues to poke through: the Code, to use an oft-cited legal image, is written on a common law palimpsest rather than a tabula rasa.

Now is 'palimpsest' a beautiful word, or what?