The screw would not fall towards Earth but maintain a similar orbit to the Space Shuttle, experiencing what is referred to as microgravity. There's no atmosphere in space to cause any resistance, and the screw would 'float' rather than fall.
The question deals with the concept of objects in free fall in outer space. In the vacuum of space, and particularly when referring to a situation involving the International Space Station (ISS) or a Space Shuttle, there is an absence of atmospheric drag, and gravity is what primarily dictates an object's motion. However, both the Space Shuttle (when it was operational) and the ISS are said to be in continuous free fall around the Earth, creating a state of microgravity inside.
This means that an object that becomes detached from the shuttle would not 'fall' towards Earth as it does on the surface. Instead, since both the screw and the shuttle are in orbit, they both are subject to the same gravitational pull and would continue orbiting unless acted on by another force. Without external forces, the screw would basically 'float' relative to the shuttle rather than fall in the traditional sense. Thus, to directly answer the question, the screw would not fall at all in relation to the shuttle, but rather maintain a similar orbit.