Anahera, 3, and mother Antonia Scott with Rapunzel doll. Anahera is still waiting on a Tangled costume of Rapunzel that was ordered five weeks ago.

Three-year-old Anahera Scott is still wondering why she didn't get to be Rapunzel for a Disney-themed birthday.

Her mother, Auckland woman Antonia Scott, had ordered and paid for a fancy dress based on the character from Disney film Tangled for her daughter two weeks before the party from Waikato-based online business, The Costume Shop, but the dress never arrived.

An automated email said her payment of $87.85 including shipping and GST, had been received and the courier service would be in touch, but about 10 days later, there had been no delivery, Antonia Scott said.

She sent off one email at two weeks, then another five days later, neither of which were answered.

"I then thought I would ring, but discovered no phone number listed on the website and alarm bells started to ring."

The Commerce Commission has launched an investigation into The Costume Shop which relates to 16 complaints it has received this year, said the commission in a statement.

"These complaints primarily relate to consumers paying for costumes which were not delivered or consumers experiencing delays in receiving costumes."

The website sports an impressive array of outfits from Sevens costumes to the Frozen's Princess Elsa to child's size Buzz Lighters and baby zombies.

However in addition to the formal complaints, multiple online reviews express dissatisfaction after they paid for colourful ensembles that never arrived, or turned up weeks later.

The Costume Shop owner Angela Flayed said she was aware of the complaints and put the delays down to a "system change with our suppliers" in June, who she would not name.

She said a banner was placed on the site warning users that there may be delays in deliveries.

However many online complaints pre-date this system change.

Online reviews for The Costume Shop dating back to June 2013 on one website rated the service as terrible, while there was one point each for OK, good and excellent.

Flayed, who has run the business since 2007, acknowledged the complaints.

"You do get a person here and there that gets ruled up and that's something I have understood."

General manager of Musical Theatre New Zealand, Kate Ghent, said she ran into trouble with the company in June after buying a $92 pair of shoes for a fancy dress event.

Ghent had looked at offshore sites Amazon and eBay before deciding to support the "local yokel" and buy the shoes online through The Costume Shop.

The shoes did not arrive and, after failing to find any way of contacting The Costume Shop through its website she found a phone number on an online directory - but it was disconnected when she rang.

"I thought I'd been had."

The payment had been processed through her credit card but her bank advised her to cancel her and her husband's credit cards.

When the shoes did not arrive after two weeks Ghent "named and shamed" The Costume Shop on her personal Facebook page.

The day after venting her frustrations online she said a box containing just the shoes - with no GST receipt or return address - was delivered to her front door by courier.

Flayed said she was prepared to work with disgruntled customers and refund where necessary.

"All I can do is fix it now. I want to fix it."

Scott thought it was unacceptable that Flayed was allowed to continue to operate considering so many others had had a similar bad experience.

"I don't want this to happen to anybody else... Anahera was so disappointed she couldn't go as Rapunzel. The idea this is happening to other people is horrible."

Scott, who made her order on August 23, said she's still heard nothing from The Costume Shop and would be seeking a refund.

Scott said she was frustrated when she struggled to find a phone number for the website, and when she found one - discovered it had been disconnected.

Flayed said the online-oriented business meant it made more sense for people to contact her through the website, so she hadn't had a phone service for about three years.

The commission advised consumers to research traders before spending money with traders.

"In general, we suggest that when buying online consumers should thoroughly review the business by searching for the seller online, talking to family and friends, checking review sites, social media and websites like Scamwatch to see what other customers have experienced."