For more information regarding Bristol-Myers Squibb Clinical Trial participation, please visit: www.BMSStudyConnect.com Inclusion Criteria: - Histologic confirmation of carcinoma of the prostate without small cell features - Documented prostate cancer progression by Prostate Cancer Working Group 3 (PCWG3) criteria while castrate - Evidence of metastatic disease documented by either bone lesions on radionuclide bone scan and/or soft tissue lesions on computed tomography (CT)/magnetic resonance imaging (MRI) - Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1 - Ongoing androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone (GnRH) agonist/antagonist or bilateral orchiectomy (i.e., surgical or medical castration) confirmed by testosterone level ≤ 1.73 nmol/L (50 ng/dL) at the screening visit - Chemotherapy-naive for metastatic castration-resistant prostate cancer (mCRPC) and have received at least one novel antiandrogen therapy (NAT) Exclusion Criteria: - Concurrent malignancy (present during screening) requiring treatment or history of prior malignancy active within 2 years prior to treatment assignment in Part 1 or randomization in Part 2 - Untreated central nervous system (CNS) metastases - Leptomeningeal metastases - Active, known or suspected autoimmune disease Other protocol-defined inclusion/exclusion criteria apply