About a week ago a girl was shot in a Maryland school. Soon after that, a police officer shot and killed the gunman. The girl was critically injured, and on life support. After a few days, the family decided to take her off life support and she died soon after. Suppose the killer didn't die. What crime would the killer be charged with? The girl has died, but technically she would probably still be alive if her parents didn't take here off life support. I think in some cases, a jury could be convinced that it would be extremely unlikely that a victim would ever regain consciousness. Many would regard this as worse than attempted murder. Do some states have a crime that is appropriate for that situation?
It would be murder (assuming the facts surrounding her getting shot would support a murder charge, of course, and it wasn't something like an accidental discharge.) The fact that she was on life support for a time is irrelevant.
Under Maryland law § 2-102 it doesn't matter how much time has elapsed:
A prosecution may be instituted for murder, manslaughter, or unlawful homicide, whether at common law or under this title, regardless of the time that has elapsed between the act or omission that caused the death of the victim and the victim's death.
It's a Wisconsin and not a Maryland case, but according to State v. Below, 799 NW 2d 95 - Wis: Court of Appeals 2011, it doesn't even matter if life support was wrongly terminated; the defendant is still guilty:
[E]ven if the Defendant can establish that the termination of Madison's life support was "wrongful" under Wisconsin Law, that wrongful act would not break the chain of causation between the Defendant's actions and Madison's subsequent death.
There are cases where a charge of murder has been brought when the victim of a shooting died more than 20 years later. The new stories at the following links give two examples, easily found with a Google Search: victim dies 20 years later
It may vary by jurisdiction, but there is precedent to charge that individual with murder. Although, it is doubtful it varies greatly because, of course, the victim was murdered.
Here's one example, from New York, where a guy was charged with numerous things including attempted murder. An assault took place on December 5. It was reported on December 13 that the victim was taken off life support and that the suspect would subsequently be charged with murder.
Here's the beginning of an article on the topic (the meat of it is behind a paywall, but the relevant point is included). The article deals with a death that happens years after the initial assault, but the opening paragraph states that a subsequent victim death can lead to a prosecutor subsequently charging the suspect with murder.
And here's a 1994 article in the NY Times where the State Court of Appeals clarifies the "delayed death" exception. This holds that, in an exception to the state's double jeopardy law,
the state's highest court ruled today that a person who has pleaded guilty to attempted murder may be charged with murder if the victim later dies.
So, to answer your question (without providing any sort of legal advice, of course), a murder charge can likely stick in the situation you described.
There is an old common law rule that if the victim survived for a year and a day, that was conclusive proof that the victim had not died of the injury and that a conviction of homicide could not be made.
However, in many jurisdictions this rule has been overturned, either by legislation or by more recent case law. In those jurisdictions, providing the death can be proved to be the result of the perpetrators acts or omissions there is no time limit.