Officers said they have received reports both nationally and in North Yorkshire of fake Census text messages being sent to residents.
These messages say that either your Census data is incomplete or that you have failed to provide any data and threaten the recipient with a fine, police said.
The text asks you to call a number or follow a link to a website to fill in your details.
North Yorkshire Police said: "Needless to say, this is a scam!
"If you receive a message like this, you can forward it on to the National Cyber Security Centre on 7726 and then delete it.
"The official Census website states that if you need to be contacted about your Census this will always be by post or by a Census officer visiting your home.
"If someone visits your home claiming to be from the Census, check their identification before providing any of your personal information."