A house near Bourne Westfield Primary Academy was targeted by burglars between Monday and 10.25am on Wednesday.
Anyone with information should call 101, quoting incident 120 of May 13.
This scam has led to victims across the UK losing many thousands of pounds, often their entire life savings.
You can also call Crimestoppers on 0800 555 111.
Meanwhile, police are warning people in Bourne to be alert after reports of several attempted phone scams in the town this week.
Callers claiming to be detectives based in Skegness are asking for bank card details because somebody is in custody on suspicion of falsely using the cards. Potential victims were then asked to hang up and redial 101 to confirm that the caller was genuine.
A Lincolnshire Police spokesman said: “This scam is a variation on recent frauds where the caller claims to be from the Metropolitan Police.
“The fraudsters keep the line open so that when the victim makes a call thinking they have got through to the police or to their bank, they are actually still speaking to the criminals.
“This scam has led to victims across the UK losing many thousands of pounds, often their entire life savings.
“Fortunately, increased awareness about the scam is helping to protect people and none of the people targeted this week fell victim to the scam.
“However, it is a reminder that scammers are still operating in our county and we should all be vigilant.”