The CA considered a petition filed by a group of voters of Galle.
Notice was issued on Kumarasinghe, the IGP, the controller of immigration and emigration and other respondents to appear before courts on October 19.
The petitioners cite provisions in the 19th amendment to the constitution which bar dual citizens from holding MP positions.
They say Kumarasinghe hold citizenship of both Sri Lanka and Switzerland.
Previously, speaking to the media, she has rejected the allegation.