Gersdorf had condemned PiS reforms of the Constitutional Court, which include changing the order in which cases are heard and how the chief justice is chosen in a move which had also drawn concern from the European Commission.
The Supreme Court supervises Poland's system of lower courts, while the Constitutional Court's main role is to check that Polish laws are compliant with the constitution.
On Thursday, several dozen PiS lawmakers called on the Constitutional Court to check whether Gersdorf's nomination in 2014 had been in line with the law, according to one of the politicians, Arkadiusz Mularczyk.
A spokesman for the liberal Civic Platform (PO) main opposition party condemned the move as a bid to "get rid of an independent chief justice and replace her with someone politically dependent on the decisions of (PiS leader) Jaroslaw Kaczynski".
"An independent Supreme Court and independent judges at all levels stand in the way of the PiS party's political strategy," spokesman Jan Grabiec added.
Critics also cite other PiS bids to consolidate power including moves to increase state control over public broadcasters.
Clashes over the judicial reforms gave rise to string of large demonstrations by a new popular movement, the Committee for the Defence of Democracy.
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