The present study aimed to investigate how hand use and the eye state affected handwriting performance. Twelve right-handed students (6 females and 6 males, aged 27.2 ± 2.4 years) completed handwriting tasks with both dominant and non-dominant hands under eyes-open and eyes-closed conditions. Handwriting tracing dynamics, handwriting quality, and legibility were measured, while electromyography signals were recorded bilaterally from the upper limb muscles. A two-way ANOVA revealed no significant interaction effects of hand use and the eye state on handwriting tracing dynamics or muscle activity. However, significant interaction effects were found for the number of intersection points (p = 0.034, ηp² = 0.129) and the legibility score (p = 0.004, ηp² = 0.205). Post hoc tests indicated greater handwriting accuracy degradation in the non-dominant hand under eyes-closed conditions, with significant differences in the number of intersection points (p = 0.016, d = 0.350) and the legibility score (p < 0.001, d = −0.130). To further explore relative differences between eyes-open and eyes-closed conditions, the ratio of change was calculated for each handwriting feature. The results showed a significantly greater change in the number of intersection points (p = 0.027, r = 0.639) and the legibility score (p = 0.012, r = −0.723) for the non-dominant hand compared with the dominant hand. These findings highlight distinct neural mechanisms underlying handwriting control, suggesting greater reliance of the non-dominant hand on visual feedback for handwriting accuracy. This study advances our understanding of motor skill learning and the acquisition of fine motor skills.