Unknown persons tried to set fire to a day-care center in the Grünau district of Leipzig over the weekend.
There had also been an arson attack on a refugee accommodation in the district over the weekend.
Refugee children from the Ukraine are cared for in the day-care center.
The State Criminal Police Office (LKA) announced on Tuesday that it would be checked whether there was a connection between the crimes.
Between Friday afternoon and Monday morning, the perpetrators are said to have tried unsuccessfully to set the kindergarten's entrance on fire.
The building was not in use at the time of the crime and no one was injured.
The facility is less than a kilometer from the refugee shelter that was attacked on Saturday night.
The LKA cannot rule out a politically motivated act.
The police are looking for witnesses.
lmd/dpa