This study is to evaluate how safe and effective ritlecitinib is in participants with non-segmental vitiligo (NSV). Ritlecitinib is studied in patients with non-segmental vitiligo. Vitiligo is a chronic acquired depigmentation disorder characterized by well-defined pale white patches of skin. Non-segmental vitiligo is an autoimmune disorder and is the focus of this study. The study will show: * if the repigmentation (the recovery of pigmentation) achieved in study B7981040 (also called the parent study) will stay the same or will further increase if you keep receiving the same study medicine (ritlecitinib 50 milligrams or placebo) * Or if more repigmentation can be achieved if you start receiving ritlecitinib 100 milligrams in this study * Or how long the repigmentation achieved during the parent study lasts if you start receiving placebo in this study. This study is seeking for participants who: * have non-segmental vitiligo (either active or stable) and * received ritlecitinib or placebo for 52 weeks in the parent study. A placebo looks exactly like the study capsule but does not contain any medicine in it. All participants in this study will receive the study medicine or placebo. The study medicine (ritlecitinib 50 milligrams or 100 milligrams) or placebo are capsules that are taken by mouth at home every day. On study visit days, you must take the medication at the study site, and not at home. Participants may receive the study medicine or placebo for up to 52 weeks. The study will look at the experiences of people receiving the study medicine. This will help see if ritlecitinib is better for treating vitiligo. Participants will be involved in this study for a maximum of 60 weeks. During this time, they will have 9 study visits during the study. Ritlecitinib 50 mg is an approved drug for the treatment of severe Alopecia Areata (a disease with similar abnormal changes in the body functions like vitiligo) in the US, EU and Japan. China, Great Britain and other market applications are pending.