A Clinical Study to Test Efficacy and Safety of Repeat Doses of CNTX-4975-05 in Patients With Osteoarthritis Knee Pain

Key Inclusion Criteria: * Male or female subjects between 40 and 95 years of age (inclusive) at the time of the Screening Visit with the ability to comply with answering the electronic diary using the study- provided tablet computers. * Confirmation of osteoarthritis (OA) of the knee. * Confirmation of the OA of the index knee. * Moderate to severe pain in the index knee associated with OA must be stable for a minimum of 6 months prior to Screening, as assessed by the investigator. * Body Mass Index (BMI) ≤45 kg/m\^2 * Must have failed 2 or more prior therapies. Exclusion Criteria: * Joint replacement surgery of the index knee at any time, or open surgery of the index knee in the past 24 months. * Prior arthroscopic surgery of the index knee within 6 months of Screening. * Any painful conditions of the index knee due to joint disease other than the OA. * Periarticular pain from any cause. * Other chronic pain anywhere in the body that requires the use of analgesic medications. * Instability of the index knee. * Misalignment (\>10 degrees varus or valgus) of the index knee on standing. * Documented history of neuropathic arthropathy or finding of bony fragmentation in the index knee with imaging. * Physical/ occupational/ chiropractic therapy for the lower extremities or acupuncture for the lower extremities within 30 days of Screening, or need for such therapy during the study. * Plans to have surgery, other invasive procedures, or IA injections while participating in the study. * Has used topical capsaicin on the index knee within 90 days of Screening. * Current use of opioids for any condition other than for OA of the index knee. * Corticosteroid injection into the index knee within 90 days of Screening. * Received IA viscosupplementation (eg, Synvisc®, Hyalgan®) within 90 days of Screening.