To achieve herd immunity to a disease, a large portion of the population needs to be vaccinated, which is possible only when there is broad acceptance of the vaccine within the community. Thus, policymakers need to understand how the general public will perceive the vaccine. This study focused on the degree of COVID-19 vaccine hesitancy and refusal and explored sociodemographic correlations that influence vaccine hesitancy and refusal. A cross-sectional online survey was conducted among the adult population of India. The survey consisted of basic demographic questions and questions from the Vaccination Attitudes Examination (VAX) Scale. Multinomial logistical regression was used to identify correlates of vaccine hesitancy and refusal. Of the 1582 people in the study, 9% refused to become vaccinated and 30.8% were hesitant. We found that both hesitancy and refusal predictors were nearly identical (lower socioeconomic status, female gender, and older age groups), except for three groups (subjects aged 45–64 years, those with approximate income <10,000 INR/month, and those residing in rural households) that showed slightly higher odds of vaccine hesitancy than refusal. We need to address the underlying sociodemographic determinants and formulate public awareness programs to address specific subgroups that are at higher risk of rejecting the vaccine and convert those who are undecided or hesitant into those willing to accept the vaccine.