This is a good question, we haven't received this in a while here at AAP so we will answer it again.

Bottom-line:  COR's (if they've been delegated this responsibility) are authorized to review and approve invoices on Firm Fixed Price (FFP) contracts.  They are authorized to review vouchers on cost reimbursement (CR), time and material (T&M), and labor hour (LH) contracts but are NOT authorized to approve them.

There are many References for this including the DoD Financial Management Regulation.  But for simpliciity I will just provide two of the primary references:

1) DoDI 5000.72 DoD Standard for Contracting Officer's Representative (COR) Certification dated March 26, 2015.  See Enclosure 6, Table - 1, Item #37, on page 25.

2) The Defense Federal Acquisition Regulation Supplement  (DFARS) 242. 803(b), which states that only the auditor (DCAA) is allowed to approve interim vouchers.  The Contracting Officer is responsible for approving the final voucher.

Hope this helps.