This is what the Manual of Cartridge Conversions says:
.38 S&W / .38 Special
Case Length .780 / 1.155
Head Diameter .386 / .380
Rim Diameter .433 / .440
Neck Diameter .386 / .379
Rim Thickness .047 / .058
It list a load of 4.7 gr Unique with a 150 gr .359 lead bullet at 890fps. It say that .38 Special cases can be used and they will fireform to fit the chamber.
Cartridges of the World has these loads:
2.5 gr Bullseye with 148 gr lead bullet at 700 fps,
3.0 gr Unique with a 158 gr lead bullet at 700 fps,
Remington factory load with 145 gr lead bullet at 685 fps.
I've got a 1970 Lyman manual that has these loads with a 150 gr lead bullet:
Powder Starting / Maximum
Bullseye 2.0gr:598fps / 2.9gr:810fps
Red Dot 2.1gr:578fps / 3.0gr:740fps
Unique 3.5gr:731fps / 4.6gr:973fps
This manual says that these loads are for solid-frame revolvers only.
I've had several S&W top breaks and have fired them with the factory ammo. I didn't shoot them enough to buy the reloading dies. If yours is a top break I would keep the loads light or use factory ammo. They are a weak design. Factory loads are not hard to find. I think Top Dollar Pawn in Jackson has several boxes.