The spokesperson told RNZ Pacific that police are still investigating, including if the woman was part of a turtle tour when the incident happened.
They said police are giving the family space while they stay at their accommodation in Rarotonga.
After the earlier death late last year, local tour company Ocean Toa Cook Islands said the New Zealand man was alone when he died and was swimming outside of tour operating hours.
“This is sad news for us all and our deepest condolences to the anau [family] and those involved,” the company said at the time.
It said the drowning was a “stark reminder” of how dangerous the water around Rarotonga could be.
“Our waters... should not be underestimated. Your individual safety should never be compromised,” the company said.
“In our tikanga and akonoanga Māori, we have suspended our tours today as a mark of respect to the family and the loss that has occurred in our waters.”
A local also told the Cook Island News the water in the area could be treacherous, saying: “It not safe to go by yourself, it is good to have a lifesaver. The sea looks beautiful, but the current is dangerous.”
A letter from another local published in the outlet said: “It’s time to stop pretending that the lagoons are safe and have ‘life guards’ always available to educate and if required rescue a person in need.”
* Additional reporting NZ Herald
