Gravitational attraction/acceleration, as you know, decays with distance from the surface of any massive object in accordance with the inverse square law. If we imagine this decay from the surface of the doughnut (at any position), let`s say on the internal "equator", then the attraction becomes much smaller very quickly as you take off towards the centre of the system, but the effects from the opposite parts of the doughnut are even less significant at any position, until we get to the centre of the hole where all attractions are equal and opposite. If we go back to the Earth/Moon system where there is a neutral point where the Earth`s field counteracts the Moon`s, then we have the same situation here and the neutral point is a point in the centre of the hole in the equatorial plane. At this position, there is no net effect in any direction as the vector sum of the fields is zero in all directions, and one would simply float at this position. One could, however, walk freely all over the surface of the doughnut without noticing the small decrease in weight on the internal equator and the slight weight gain on the outside equator.

At the outside equatorial plane, we have a thin "disc" of space, spreading towards infinity, where the gravitational effects are the same as if the doughnut where spherical.

As we move up, over and around from this imaginary disc and curl towards the neutral position, then through an axial section cutting the doughnut, we see two effects superimposed. The first is the "normal" gravitation from the immediate part of the doughnut, but superimposed on this is the gradually increasing effect from the opposite section of the doughnut. I ignore the effects to the sides of our considered section as these are equal and opposite and therefore cancel.

The distribution of the gravitational acceleration around this curve is one of a normal spherical planetary attraction, but skewed slightly towards the other side of the doughnut. The equivalent gravitational force will therefore vary slightly, as previously described, with the maximum on the external equator and the minimum on the internal equator.

I trust this helps.