Two benches have been damaged at Hathersage Bowls Club.
One was broken and the other set fire to sometime between January 2 and January 9.
PCSO Anthony Boswell, of the Hathersage Safer Neighbourhood Policing Team, is investigating the crime.
He said: "We have had reports of youngsters in the area during the evenings that week and they may have information about the damage which was caused.
"If you think you can help in any way, please get in touch."
You can call PCSO Boswell on 101, quoting reference number 19*22993.