Directional perforation fracturing of horizontal wells in coal seam roof is one of the important technologies for efficient extraction of coalbed methane (gas) in broken soft coal seams. Mastering the characteristics of crack initiation can provide theoretical support for fracturing scheme design. Considering the development of coal seam and its roof bedding, combined with the distance between the horizontal well and the coal seam, the fracturing geological engineering model was constructed. The water pressure discriminant of different initiation modes was deduced and verified. The variation law of crack initiation pressure under different crack initiation modes was analyzed, and the initial shape of cracks under different working conditions was predicted. The results show that there are four working conditions for directional perforation fracturing of roof horizontal wells. The water pressure required for crack initiation of coal seam and structural weak surface (bedding and interface) is less than that of roof. The first crack initiation point of directional perforation fracturing of roof horizontal well is located at the root of perforation hole, which is easy to break again at the position of structural surface and coal seam. The in-situ stress field conditions affect the crack initiation sequence at different positions. The development of the bedding in the roof increases the crack initiation point in the process of crack propagation, affects the crack propagation path, and makes the crack morphology in the roof more complex. Under most conditions, the perforation hole enters the coal seam, which is more conducive to coal seam cracking. The related research enriches the theory of roof fracturing and contributes to the promotion of horizontal well technology in coal seam roof.