Background: It is crucial to evaluate children’s motor coordination and strength to identify possible motor deficits on the right or left side of the body. However, whether a distinction exists in children aged 3–6 must be clarified. The goal of the current research was to investigate the differences in motor skills between preschool boys and girls, dominant and non-dominant hands or legs, in children of preschool age. (2) Methods: The present study was conducted on a sample of children (boys, n = 52; girls, n = 52; age range, 3–6 years). Three motor tests evaluated on both sides of the body served as the sample of factors used to measure athletic performance. Leg tapping (15 s), hand tapping (15 s), and a maximal hand grip strength (HGS) test kg. (3) Results: The study’s findings show no statistically significant variations in preschool boys’ and girls’ motor skills. Preschool girls had better results in the right leg tapping than preschool boys t (98) = 2.08; p ≤ 0.04. We found a significant difference between genders aged 3–4, 4–5, and 5–6 years. No correlation was found between the girls’ three variables and age. A small but significant positive correlation was found between dominant hand tapping and age r2 (52) = 0.21; p ≤ 0.01, dominant leg tapping and age r2 (52) = 0.20; p ≤ 0.01 and dominant HGS and age r2 (52) = 0.17; p ≤ 0.01. No noticeable differences were identified when comparing the dominant side with the non-dominant side in each group. The results show that most children prefer to use their right hand and right leg as their dominant sides. (4) Conclusion: The authors of this study focus on the functional (frequency of movements) and dynamic (differences in muscle strength between body sides) elements of asymmetry. Future studies should examine the influence of morphology on performance with the dominant or non-dominant body side.