Welcome to the forum.
The headliner is a plywood panel, covered in padded fabric, glued to the plywood.
There are perimeter screws to retain the plywood to the ceiling. Sometimes there are screws placed closely together.
The screws are covered w/ the padded fabric. That padded fabric is not glued to the plywood at the screw locations. The padded fabric is just pulled to cover the screws and tucked into the gap.
The best / only way to locate the screws is to push against the padded fabric to feel the screw heads, then pull back the fabric to expose the screws for removal.
