It’s not clear what is meant by “target objects”.
The title of your post would suggest you’re asking if only Static colliders (colliders without Rigidbody) are supported and detected queries which would make the physics engine useless if that were the case.
Despite the misleading title, that’s not what is happening so you’re doing something else wrong. No idea what that is.
I would suggest clarifying what you’re doing here by providing some specific details. Maybe some script using code-tags might help. It might then be clear on what you’re doing wrong.
NOTE: It’s not clear if this is 2D or 3D physics.