Digital contact tracing can limit the spread of infectious diseases. Nevertheless, there remain barriers to attaining sufficient adoption. In this study, we investigate how willingness to participate in contact tracing is affected by two critical factors: the modes of data collection and the type of data collected. We conducted a scenario-based survey study among 220 respondents in the United States (U.S.) to understand their perceptions about contact tracing associated with automated and manual contact tracing methods. The findings indicate a promising use of smartphones and a combination of public health officials and medical health records as information sources. Through a quantitative analysis, we describe how different modalities and individual demographic factors may affect user compliance in providing four key pieces of information to contact tracing.