While they mention doing an assessment they do not specify what that assessment is. That said, they are the mining company, so it should be quite straightforward to know if they are sourcing from CAHRAs. I have therefore marked this as "yes".
"As per Part A – Conflict Assessment, Barrick concluded that we do not breach any international sanctions and we have no operations considered to be in ‘conflict-affected or high-risk’ areas according to the Standard. As none of Barrick’s operations are in ‘conflict-affected or high-risk’ areas, Part B – Company Assessment and Part C – Commodity Assessment are not required.
Barrick also complies with Part D – Externally Sourced Gold Assessment. We source gold from third-parties at an operation in the United States of America for toll milling and scrap purchasing. In accordance with the Standard, Barrick has implemented the risk-based due diligence procedures outlined in the Gold Supplement to the OECD Due Diligence Guidelines for Responsible Supply Chains of Minerals from Conflict-Affected and High-Risk Areas to determine that there are no links between the gold and gold-bearing material purchased or milled and areas assessed to be conflict-affected or high-risk. Barrick is therefore in conformance with Part D of the Standard." P. 2