This is a Phase 1b, open-label, two-period, randomized crossover study in adult male and female participants with painful knee osteoarthritis.

Key Inclusion Criteria:

• Body mass index (BMI) between 18.0-35.0 kg/m^2
• Subject has moderate to severe painful osteoarthritis in one knee while walking (index knee); contralateral knee may or may not have osteoarthritis, pain should be none to mild in the non-index knee
• Confirmation of the OA of the index knee: American College of Rheumatology (ACR) diagnostic criteria
• Subject has intact skin at the location of the dosing sites (patch or injection)

Key Exclusion Criteria:

• Subject has any other form of arthritis, such as, but not limited to, rheumatoid arthritis, psoriatic arthritis, gout, systemic lupus erythematosus, etc.
• Subject has a dermatological condition that may contraindicate participation, including any compromise in skin integrity at the CNTX-4975-05 injection site or the Qutenza® skin application site, e.g., severe or cystic acne, psoriasis, eczema, atopic dermatitis, active or treated cancer, etc.