Cold-blooded murder was always illegal and carried with it legal punishment, from the earliest surviving medieval law code we have through the entirety of the medieval era. A person would be acquitted if the murder was found to be done in self-defence. One could also be found innocent on grounds of insanity and usually if the murder was ruled to have been committed by accident or through negligence. The legal concept of manslaughter developed quite a bit over the course of the medieval era, so as far as that goes, it really depends on what point in the Middle Ages you are considering.
The medieval period in England spanned around 1,000 years, and as one could expect, law codes and the legal system as a whole underwent significant changes and development over ten centuries. The consequences for being found guilty of murder were quite different in the early 7th century law code of King Æthelberht from those attendant to the laws which were in place when Henry Tudor (Henry VII) ascended the throne in the late 15th century.
In Æthelberht’s law code, a person would be fined a substantial amount of money, either 50 or 100 shillings, if found guilty of murder. Keep in mind, most day labourers were paid in what amounted to pennies per week. The law code uses the term ‘man’ ("If a man slay another…"), but ‘man’ is gender-neutral in Old English (see citation below of Anne Curzan’s book).
Up to the 13th century, a man accused of murder could face trial by jury or trial by ordeal, the latter of which could very well kill him in the process. After the 13th century in England, trials were conducted by a jury of twelve men. Women were not permitted to be jurors. Depending on the jury’s sympathy, a man convicted of murder could face the death penalty. If a woman were to murder her husband, however, she would be tried not for ‘simple murder’ (as would a man accused of murdering his wife) but for ‘petty treason’ after the enactment of the Treason Act of 1351.
Curzan, Anne (2003). Gender Shifts in the History of English. Cambridge University Press.
Oliver, Lisi. The Laws of Æthelberht: A student edition, Louisiana State University, at http://www.oenewsletter.org/OEN/print.php/essays/oliver38_1/Array
Briggs, John (1996), Crime and Punishment in England: An introductory history, London: Palgrave Macmillan.
Blackstone, William; Christian, Edward; Chitty, Joseph; Hovenden, John Eykyn; Ryland, Archer (1832). Commentaries on the Laws of England, vol. 2, (18th London ed.), New York: Collins and Hannay.
Green, Thomas A. (1976). The Jury and the English Law of Homicide, 1200-1600. University of Michigan Law School.
Green, Thomas A. (1972). Societal Concepts of Criminal Liability for Homicide in Medieval England. University of Michigan Law School.
Edit: grammar