Constraints sets (csets) are not assigned at the net level except in the simplest use model.
Electrical constraints (ECsets), which have the simplest use model, could be assigned at the net level by an ECset. You need to remmeber that an ECset is just a grouping of electrical constraints so while a net might have a ECset assigned it also may have an override constraint such as IMPEDANCE assigned directly. In the case of directly assigned Ecsets if you have the net dbid (net) then the ecset name is obtained via:
Alternatively, the net may have an ECset without an IMPEDANCE constraint but it is a member of BUS which is asssigned a different ECSET with an IMPEDANCE rule. When Allegro resolves, for impedance on the net it will obtain the value off the ECSET on the Bus. A Skill API can be used to obtain the electrical rule that impacts a net via:
Physical, spacing and same net csets have a more complex use model. Constraint regions, layers,netclasses and in some cases most conservative impact the constraint resolution for these domains. If you are directly assigning csets to nets then just like with ecsets you can obtain the cset on the net via the property method. Example if a net has a physical cset assigned then given a net dbid the pcset name is
Spacing and same net use can be obtained the same way via their properties.