Police received eight reports of bogus kidnap calls on Monday, after a four-month lull.
Alerting the public to the ruse on Wednesday, police said the callers threatened to harm the family member if money was not transferred to them.
In some instances during the phone conversations, cries of help could be heard from the purported kidnap victim to make the threat seem genuine.
"All the allegations were found to be untrue and no one has been kidnapped," said a police statement on Wednesday.
"Police would like to caution members of the public from falling prey to these scams. They are advised to remain calm and to call the Police immediately if they are approached in a similar manner."
On Aug 24, similar phone calls were made to several unrelated persons, alleging that one of their family members had been kidnapped and would be harmed, if money was not transferred.
No one had been kidnapped.
But at least one family was cheated of $50,000.
The culprit is still at large.
Police are investigating the scam calls.