In this situation, putting magic aside for the time being, there are still certain fundamental investigative methods that may be applied. These are often classified as forensics and human intelligence. Since most murders are still solved within the first two days of the crime, necromancy would only be employed in the most challenging instances if there was a minimum amount of time that had passed before it could be used.
Human Intelligence
In essence, human intelligence involves having the detectives question the suspects and witnesses informally anywhere they might encounter them or professionally in an interview room. Since hundreds of years ago, questioning suspects and witnesses hasn't altered much, and it isn't technology-dependent either. A good investigator continues to identify and seek discrepancies in a subject's dialogue and ascertain who has good alibi or not, even if the investigators forego using torture for any reason, such as their recognition that confessions or information obtained in this way is unreliable or simply because it is illegal.
Forensics
Even though there wouldn't have been as many scientific tests available in pre-industrial society, forensics has been around for several centuries in some sort. This nevertheless provides a variety of choices:
Autopsy. A victim of murder is likely to show signs of the methods used to bring about their demise. This could be poison remains, tool marks from a blunt or sharp object, or anything else. It is probable there are forensic magicians and forensic doctors, who may or may not be the same individual, where magic may exist and be used to murder.
crime scene investigation. Blood can be spilt and create specific patterns that reveal how it was spilled, the order in which events happened, and even the outline of the murderer in a void in the blood-spray pattern. 917
The murderer could leave behind evidence of himself, such as hair, fibers, footprints, etc., and may also remove evidence from the crime scene. The relevance of such evidence would be diminished, but not eliminated, and it might be harder to link the two than it is presently.
Magic
While necromancy is fairly restricted, there might be other magic that can be used to verify a witness's or suspect's claims. Such spells in fantasy usually provide a true/false reading, however more complex ones may be able to provide a partial-truth and/or deceptive response signal. This would only reveal what the spell's target thought to be true, of course, and there may be spells that change a person's recollection of past events so they can tell a "lie" and still come out as truthful when questioned.
If the murderer is exceptionally cunning, he or she may even change his or her own recollection of the incident such that, by the time the investigation hits him, the suspect may no longer be aware that the crime was done and may have an altogether different recall of the incident. Investigators must take this into consideration if a suspect is a magician, and if the suspect is not a magician, the magician who altered the victim's memory may be found and called to testify. It is extremely conceivable that a practitioner could be convinced to testify against a criminal in order to avoid being charged as an accessory to the crime if it were lawful to modify someone's memory at their request. However, doing so would require the investigators to track down the concerned practitioner.
The law of contagion is another recurring theme in magic; if two objects are joined, they will stay connected, albeit the length of time that this connection lasts varies depending on the situation. The missing piece of an object or collection can be miraculously found via the law of contagion, just like the individual whose hair, fingernail, etc. was left at the crime scene. It can just be dowsing or it might be some kind of visual scrying. Even when restricted to dowsing, a skilled dowser may trace a murderer's steps after they left a crime scene for a fair distance—likely just as far as the point where they crossed moving water in a vessel or by swimming. 59