Designer David Rockwell is among six trustees that have stepped down to protest Caroline Baumann's resignation as director of the Cooper Hewitt after it was reported her departure followed an investigation into her wedding.

The six trustees have argued they should have been consulted before it was decided Baumann should resign on 7 February, according to The New York Times. She is reported to have stepped down following an investigation into her conduct in acquiring the wedding dress and venue for her 2018 wedding.

"We all serve on the board because we share the principles of the institution and the values of its leadership," Rockwell said in his letter of resignation, according to the New York Times. "I cannot in good conscience continue on the board given how Caroline's dismissal was handled."

The five board members that join Rockwell include RadicalMedia chief executive Jon Kamen, Neuberger Berman Foundation founder Francine S Kittredge, entrepreneur Avi N Reichental, author Kurt Andersen and philanthropist Judy Francis Zankel.

According to the New York Times report, Zankel questioned whether the investigation was sexist in her resignation letter to the New York museum. "Can you imagine all this brouhaha about a dress and a wedding directed toward a man in the same position?" she asked. "I think not."

Investigation focused on amount Baumann paid for a wedding dress

The New York Times reported investigation focused on the amount Baumann paid for a wedding dress from Samantha Sleeper.

The fashion designer told the paper she had been questioned by federal agents over the cost of the dress she custom made for Baumann, which was reportedly much cheaper than her other designs. She said it was less expensive because it was a simple cocktail dress.

Other queries were raised regarding the location of Baumann's wedding at East Hampton's LongHouse Reserve – a non-profit sculpture garden run by textile designer Jack Lenor Larsen.

Lenor Larsen, who is a friend of Baumann, did not charge her for the use of the property. Baumann allegedly did not report this as a gift and then allowed the non-profit to hold meetings in a Cooper Hewitt conference room.

Considered the country's most significant design museum, Cooper Hewitt, Smithsonian Design Museum is partly funded by the US government and donations from its board members and other patrons.

Her actions reportedly came at odds with the museum's conflict of interest policy, which states "employees shall not solicit or accept any gift from any source that is, or appears to be, offered because the employee holds a Smithsonian position or may have influence within the Smithsonian".

Procedure is "beyond unfair" according to Yves Behar

Many others in the design community have expressed anger about the way Baumann's departure was handled.

Designer Yves Behar tweeted: "This is beyond unfair, targeting a woman director in a biased investigation about nothing is a scandal."

Behar posted the comment in response to a tweet by architecture critic Mark Lamster, which described the actions ahead of her sudden resignation as "disturbing news".

Baumann was named director in 2013 and oversaw the strategic direction and managing the renovation of the Carnegie Mansion – Cooper Hewitt's home in Manhattan's Upper East Side – and the reinstallation of its galleries.

The project included a renovation led New York's Gluckman Mayner Architects and architecture firm Beyer Blinder Belle, new fittings by architects Diller Scofidio + Renfro and a rebranding by Pentagram.

"Baumann has been a passionate voice for design, and much has been accomplished during her tenure," said the Cooper Hewitt in a statement following her resignation.

Her other projects completed as part of her tenure include overseeing the museum's sixth design triennial, called Nature. She said the showcase would show "how designers can save the planet", in an interview with Dezeen.

John Davis, who is the Smithsonian's provost/under secretary for museums, education and research, is temporarily taking over her position, while the New York museum searches for a replacement.

Dezeen contacted Cooper Hewitt but the organisation said it was unable to comment.