Between Thursday, June 27 and Sunday, June 30, 150 litres of fuel oil was stolen from a property on Dams Lane, in Belchford.
According to police, unknown persons had also been reported acting suspiciously in the Baumber area by entering several gardens after dark.
Then sometime on Tuesday, July 2, wooden supporting planks were stolen from around a grave that had been dug at Wragby Cemetery on Cemetery Lane.
On the same day chainsaws were stolen from a workshop at Horncastle Road, in Hatton.
A Lincolnshire Police spokesman said: “Report any suspicious activity via our non-emergency number 101 and 999 in an emergency. Thank you for continued support in the community.”