Use the following options to set what happens when you select Modify > Convert > Polygon Edges to Curve.
Sets the type of curve that results once the selected edges are converted.
Creates a curve with disconnected start and end points.
Creates a curve with connected start and end points. If the selected edges do not form a closed loop, Maya will automatically connect the two open endpoints.
Creates a periodic curve if the selected edges form a closed loop. Creates an open curve otherwise.
Causes the curve to follow the smoothed preview of a mesh rather than the base cage mesh. You can toggle the various Smooth Mesh Preview modes (hotkeys 1, 2, 3) to see the curve in various smooth forms.
The higher the Curve Degree, the more control you have over the curve’s smoothness. The default setting (3 Cubic) works well for most curves.