What is the correct term for 'misleading' investigations?

Consider, draw/drag a red herring across the trail/path/track

red herring

Something intended to mislead or divert attention from something else; from the old practice of dragging a herring across a track to confuse tracking dogs. Dictionary of Unfamiliar Words

The purpose of her trip to Wentworth was to hide there the dead lady's golf clubs – left-handed clubs, the attaché-case being a red herring to put the police off the trail. Murder in the Mews

set up someone [to be the fall guy]

informal Make an innocent person appear guilty of something: suppose Lorton had set him up for Newley’s murder? ODO

More than seventy years after Bruno Richard Hauptmann was executed for the kidnapping and murder of the two-year-old son of aviation hero Charles A. Lindbergh, some students of what was known as "the crime of the century," which the famed muckraking journalist H. L. Mencken termed the greatest story since the Resurrection of Christ, believe that Hauptmann was in fact the victim of a conspiracy involving faked evidence to set him up to be the fall guy. History's Greatest Conspiracies

This is commonly known as an attempt to put/throw them off the scent, an allusion to trying to misdirect sniffer dogs sent to track the criminal.

Throw someone off the scent Mislead someone in the course of a search or investigation - ODO

You could consider obstruction of justice:

Obstruction may consist of any attempt to hinder the discovery, apprehension, conviction or punishment of anyone who has committed a crime. The acts by which justice is obstructed may include bribery, murder, intimidation, and the use of physical force against witnesses, law enforcement officers or court officials.

[Ohio State Bar Association]

Its definition from West's Encyclopedia of American Law, edition 2:

A criminal offense that involves interference, through words or actions, with the proper operations of a court or officers of the court.

The integrity of the judicial system depends on the participants' acting honestly and without fear of reprisals. Threatening a judge, trying to bribe a witness, or encouraging the destruction of evidence are examples of obstruction of justice. Federal and state laws make it a crime to obstruct justice.

Common law jurisdictions other than the United States tend to use the wider offense of Perverting the course of justice

Perverting the course of justice is a criminal offence in England and Wales. The offence is committed when a person prevents justice from being served on him/herself or on another party.

[Wikipedia]

Are you looking for

Frame - verb - to contrive the evidence against an innocent person so that a verdict of guilty is assured