I have an application with co-applicants. The Applicant has a primary residence and the residence securing this loan will not be this persons primary residence. It will be the co-applicants primary residence. Do I mark the HMDA LAR as Owner-Occupied or Non-Owner Occupied?

If the owner of the property lives there as their primary dwelling, it's reported as owner occupied. Who the borrower is does not play into the decision of how to report occupancy status.

If the co-applicant is an owner of the property, then it would be owner occupied.

Under the current rules, you report the OWNER occupancy. Even if a non-borrower was pledging their primary residence as collateral, you would report as owner occupied. Now in 2018, the rules are changing this field to applicant occupancy, which should clear up some of the confusion (hopefully).