Beckett reportedly brought his wife ashore, but she was not able to be revived.
Police announced in June the matter was being treated as a homicide.
Beckett was a Napier city councillor from 1998 to 2001, and ran a tourism business taking Unimog tours to Cape Kidnappers.
He has four children in New Zealand with ex-wife Wendy Sail, who said yesterday she was aware of the arrest, but did not want to comment. She said it was traumatic for their children.
Napier Mayor Barbara Arnott, who spent one term with Beckett on the council, said yesterday she knew her former colleague was facing charges.
"He was a one-term councillor, which clearly for the city and himself was enough," she said.
A former Karamu High School student, Beckett stood on a platform of opposing the National Aquarium of New Zealand and exposing council corruption.
He did not stand for re-election in 2001, and later moved to Canada, where it's understood he married Ms Letts Beckett seven years ago.
Ms Letts Beckett taught at Dapp Elementary School near Edmonton, Alberta, for 27 years, while Beckett was a school bus driver for Pembina Hills Regional School Division. They lived in Westlock, 45 minutes' drive from the school.
Her family issued a statement through police after Beckett's arrest, saying they now believed the investigation to be over.
"As a family, we're waiting for the justice system to take its course. Please respect our family's privacy as we remember the anniversary of Laura's death."
Wendy Scinski, principal at Dapp Elementary School, told Hawke's Bay Today that Dapp was a small community "very much" saddened by her death.
"We've lost someone very special."
Ms Scinski said she didn't know whether news of Beckett's arrest "opens up anything new".
"It just takes time because she was so special."
She described Ms Letts Beckett as "a wonderful teacher" who had spent all of her teaching years at the school.
"She was a very special lady and a wonderful teacher and we miss her. She was honest, sincere and a caring person. People are just saddened by the loss."
Friend Michelle Wolfe posted on a tribute site for Ms Letts Beckett about meeting the couple last year.
"I had the privilege of meeting dear Laura this summer at the lake. With her husband, the best bus driver in the world, she graciously invited the entire bus route of families out to play in and on the water, see the wildlife together and enjoy a meal with excellent company," she wrote.
Peter Beckett's career
* Peter Beckett was one of four men elected to the Napier City Council for the first time in 1998, in one of the most hotly contested elections in the city's history.
* Using caricatures mocking election opponents in a sophisticated campaign with support from incumbent first-term councillor John Harrison, he stood opposing the National Aquarium project, and claimed he could expose corruption within city administration.
* In the citywide voting of the day, he snuck in just 92 votes ahead of the highest-polling unsuccessful candidate, one of three who lost their seats in the poll.
* A former Karamu High School pupil, Beckett was at the time essentially a Hastings person who moved to Napier for business, including Unimog Adventure Tours from the city to Cape Kidnappers, which he started after buying an ex-army vehicle auctioned at less than a quarter of its value. He was also running a gift-pack marketing business and an antique, brass and silverware business.
* He had embarked on a career path as a Customs officer in Wellington, then spent 12 years in management with NZI insurance, and a period promoted to its office in Whangarei.
* He and first wife, Wendy, bought a Bay of Plenty kiwifruit orchard and restaurant, but they moved back to Hawke's Bay about 1993, he told Napier's Daily Telegraph at the time of his election success.
* His own parents are understood to have died by his early 20s, at which time he came into ownership of a house in Bennett Rd, Waipatu.
* Claiming involvement in an array of sports and leisure organisations, it was his first venture into politics and he wanted to ``shake the mats out'' at the council and would become known as ``a bit of a stirrer''.
* Councillors and administrators of the era contacted yesterday by Hawke's Bay Today did not want to put their names to comments. Commonly initially speechless, they offered concern for his family but said Beckett did not deliver at the council table _ his regular ``punching'' at the corruption issue established nothing, one said, and it did not stop the aquarium project as he purported it would.
* Barbara Arnott, who spent one term with Beckett on the council and became mayor in 2001 when he did not seek re-election, said yesterday she had previously become aware of the arrest.
``The internet is a pernicious thing,'' she said, explaining she had not mentioned it to anyone else because of her concern for Beckett's family still in New Zealand.