The law of the land, they are apparently overworked and/or understaffed to the point that they need Private Constables such as Eva's group.

The National Police operate across the Great Republic, and have the authority to investigate any and all crimes that occur within the empire. They are not a "secret police", they are more akin to mixture of a police force and national guard. In times of war, they come under the jurisdiction of the Republican Army and operate as military police.