Dysgraphia (D) is a complex specific learning disorder with a prevalence of up to 30%, which is linked with handwriting issues. The factors recognized for assessing these issues are legibility and performance time. Two questionnaires, the Handwriting Proficiency Screening Questionnaire (HPSQ) for teachers and its modification for children (HPSQ-C), were established as quick and valid screening tools along with a third factor – emotional and physical well-being. Until now, in the Czechia, there has been no validated screening tool for D diagnosis. A study was conducted on a set of 294 children from 3rd and 4th year of primary school (132 girls/162 boys; Mage 8.96 ± 0.73) and 21 teachers who spent most of their time with them. Confirmatory factor analysis based on the theoretical background showed poor fit for HPSQ [χ2(32) = 115.07, p < 0.001; comparative fit index (CFI) = 0.95; Tucker–Lewis index (TLI) = 0.93; root mean square error of approximation (RMSEA) = 0.09; standard root mean square residual (SRMR) = 0.05] and excellent fit for HPSQ-C [χ2(32) = 31.12, p = 0.51; CFI = 1.0; TLI = 1.0; RMSEA = 0.0; SRMR = 0.04]. For the HPSQ-C models, there were no differences between boys and girls [Δχ2(7) = 12.55, p = 0.08]. Values of McDonalds’s ω indicate excellent (HPSQ, ω = 0.9) and acceptable (HPSQ-C, ω = 0.7) reliability. Boys were assessed as worse writers than girls based on the results of both questionnaires. The grades positively correlate with the total scores of both HPSQ (r = 0.54, p < 0.01) and HPSQ-C (r = 0.28, p < 0.01). Based on the results, for the assessment of handwriting difficulties experienced by Czech children, we recommend using the HPSQ-C questionnaire for research purposes.