Schröder-Köpf raised eyebrows in March when she beat a Social Democrat veteran for selection to stand for the party in a Hannover seat.
Since then her office windows have been broken with thrown stones twice.
“So far we don’t know if there is a connection between the two deeds, but we are investigating,” said a police spokesman.
An off-duty police officer noticed her office windows had been smashed at the beginning of August.
The 49-year-old former journalist posted about the attack on her Facebook page on Tuesday, just saying “stones at the constituency office again.”
Gerhard Schröder was German Chancellor for the Social Democrats from 1998 until 2005, during which time Schröder-Köpf was not particularly active politically.
But this spring she mounted the political stage in her own right, winning the Social Democrat nomination for the Hannover-Döhren seat in next January’s state election.
She and Schröder has been targeted by those campaigning for the jailed Russian punk band Pussy Riot, as they famously have a very close personal relationship with Russian president Vladimir Putin.