What is the test for presenting evidence of third party culpability in a criminal case?

A criminal defendant has a right to present evidence of third party culpability if the evidence is capable of raising a reasonable doubt about the guilt of the defendant. (People v. Hall (1986) 41 Cal.3d 826, 833.) This rule does not require "that any evidence, however remote, must be admitted to show a third party's possible culpability. . . . [E]vidence of mere motive or opportunity to commit the crime in another person, without more, will not suffice to raise a reasonable doubt about a defendant's guilt: there must be direct or circumstantial evidence linking the third person to the actual perpetration of the crime." (Ibid.)