Code sections cited in this answer are to the New Mexico Criminal code, Chapter 30 as they were in my answer to the linked question, and to chapter 59A.
Neither the landlord (whom I will cal LL) , nor any ordinary citizen, is legally required to report information that s/he may have about a crime to the police or other authorities. LL cannot actively conceal or destroy or tamper with evidence (section 30-22-5. of the NM code), nor assist the criminal by more than silence which would be a crime iunder section 30-22-4, Harboring or aiding a felon.
If the police question LL about the crime, s/he should not lie. Apparently lying to officers during an investigation is not a crime in New Mexico, although filing a false crime report is, under section 30-39-1. If LL were to make an insurance claim while omitting or misstating a materiel fact (such as that LL knows who broke in) that would be a violation of Section
59A-16-23 paragraph (2) which prohibits:
for the purpose of obtaining money or benefit, present or cause to be presented a false or fraudulent claim or proof in support of such a claim for payment of loss under a policy
I am not sure if LL owes an affirmative duty to the tenant. If LL does owe such a duty, the tenant may have grounds to sue LL if LL fails to help the tenant recover the stolen property, but it is probably not a criminal matter.