Can a jury consider a defendant's "consciousness of guilt" in determining their guilt?

The trial court instructed the jury on consciousness of guilt. The instruction provided in part: "If the defendant made a false or misleading statement before this trial relating to the charged crime, knowing the statement was false or intending to mislead, that conduct may show he was aware of his guilt of the crime and you may consider it in determining his guilt." Appellant maintains that this instruction was erroneous because "there was no basis upon which to conclude [his] statements to the police were false." A consciousness of guilt instruction is proper only if "there is 'evidence in the record which, if believed by the jury, will sufficiently support the suggested inference' " of consciousness of guilt. (People v. Ramirez (2006) 39 Cal.4th 398, 456.)