Dispatchers and troopers from around the state have been contacted by concerned citizens about unusual phone calls they have received, the department said.
The phone calls are from people claiming to be from the Connecticut State Police, among other agencies or organizations.
In some cases, scammers ask callers to deposit a check they provide and then wire the money from that account.
In other calls, scammers insist that consumers make a decision and provide private information immediately.
"Resist these calls by simply hanging up," the department said. "Citizens need to be pro-active in minimizing the chance that they will be scammed."
The department is also reminding consumers to always follow this vital safety rule: "Never, never, never provide critical private information over the phone."
All official agencies including the IRS, a bank or other government agency always contact the person in writing.
"Your bank account numbers, Social Security numbers, and other identification numbers should be kept completely private," they added.
Hang up on any suspicious calls.
To report suspicious calls or scammers, contact 1-877-FTC-HELP or visit ftc.gov/complaint. You can also contact your local police.
Click here to follow Daily Voice Fairfield and receive free news updates.