Smartphone-based monitoring in natural settings provides opportunities to monitor mental health behaviors, including suicidal thoughts and behaviors. To date, most suicidal thoughts and behaviors research using smartphones has primarily relied on collecting so-called "active" data, requiring participants to engage by completing surveys. Data collected passively from smartphone sensors and logs may offer an objectively measured representation of an individual's behavior, including smartphone screen time. This study aims to present methods for identifying screen-on bouts and deriving screen time characteristics from passively collected smartphone state logs and to estimate daily smartphone screen time in people with suicidal thinking, providing a more reliable alternative to traditional self-report. Participants (N=126; median age 22, IQR 16-33 years) installed the Beiwe app (Harvard University) on their smartphones, which passively collected phone state logs for up to 6 months after discharge from an inpatient psychiatric unit (adolescents) or emergency department visit (adults). We derived daily screen time measures from these logs, including screen-on time, screen-on bout duration, screen-off bout duration, and screen-on bout count. We estimated the mean of these measures across age subgroups (adults and adolescents), phone operating systems (Android and iOS), and monitoring stages after the discharge (first 4 weeks vs subsequent weeks). We evaluated the sensitivity of daily screen time measures to changes in the parameters of the screen-on bout identification method. Additionally, we estimated the impact of a daylight time change on minute-level screen time using function-on-scalar generalized linear mixed-effects regression. The median monitoring period was 169 (IQR 42-169) days. For adolescents and adults, mean daily screen-on time was 254.6 (95% CI 231.4-277.7) and 271.0 (95% CI 252.2-289.8) minutes, mean daily screen-on bout duration was 4.233 (95% CI 3.565-4.902) and 4.998 (95% CI 4.455-5.541) minutes, mean daily screen-off bout duration was 25.90 (95% CI 20.09-31.71) and 26.90 (95% CI 22.18-31.66) minutes, and mean daily screen-on bout count (natural logarithm transformed) was 4.192 (95% CI 4.041-4.343) and 4.090 (95% CI 3.968-4.213), respectively; there were no significant differences between smartphone operating systems (all P values were >.05). The daily measures were not significantly different for the first 4 weeks compared to the fifth week onward (all P values were >.05), except average screen-on bout in adults (P value = .018). Our sensitivity analysis indicated that in the screen-on bout identification method, the cap on an individual screen-on bout duration has a substantial effect on the resulting daily screen time measures. We observed time windows with a statistically significant effect of daylight time change on screen-on time (based on 95% joint confidence intervals bands), plausibly attributable to sleep time adjustments related to clock changes. Passively collected phone logs offer an alternative to self-report measures for studying smartphone screen time characteristics in people with suicidal thinking. Our work demonstrates the feasibility of this approach, opening doors for further research on the associations between daily screen time, mental health, and other factors.