Appraisal forms, import applications, reference materials. To that usual array of tools a museum might harness in assessing donated artifacts, some museums in Southern California appear to have added one more, according to investigators’ affidavits: a wink and a nudge.

Affidavits related to search warrants executed at four Southern California museums on Thursday say that staff members at two of the four museums worked closely with the main targets of the investigation, visiting a storage locker maintained by a smuggler of stolen antiquities and meeting with the sellers of stolen goods — even while acknowledging that the artifacts headed for the museums might be tainted.

All the activity is said to have taken place even after the emergence of high-profile investigations into the sale and acquisition of stolen artifacts to museums around the world, including the J. Paul Getty Museum here. The picture painted in the warrants suggests that none of this deterred the participants in the transactions, which were the subject of a five-year undercover investigation by federal investigators before being made public this week.