Determine _____ or not a crime has in fact been _____ and, if so, what type of crime.

The correct choice is the one that uses "whether," as it appropriately introduces a condition that requires investigation or determination. In legal terminology, "whether" is often used to indicate that a decision must be made about the existence of a condition or fact—in this case, whether a crime has occurred.

Additionally, "committed" fits contextually, as it refers to the act of carrying out a crime, which is a functional term used in law enforcement and legal discussions about crime. This pairing conveys the necessary legal implications—making it clear that the focus is on determining not only if a crime occurred but also its classification.

The other options, while they include relevant verbs, do not capture the nuanced legal phrasing required here. "If" implies a simpler conditional statement rather than the more complex legal examination that “whether” connotes. Likewise, "weather" is semantically incorrect in this context, as it pertains to atmospheric conditions rather than crime analysis.