(CNN) A British family has filed a complaint with the Department of Homeland Security over their detention by US immigration authorities, after saying they accidentally crossed the US border while vacationing in Canada, an account that has been strongly disputed by US officials.

The family of seven, which includes a three-month-old baby, were detained earlier this month. They said that they ended up in the US after taking a wrong turn from British Columbia into Washington.

A senior US Customs and Border Protection (CBP) official, however, told CNN that by all appearances on the ground, the family was trying to get into the US undetected.

In the complaint, the family said they have been "traumatized" by the experience. In a sworn statement, the family described the baby being forced to sleep on a "filthy concrete floor" in "frigid temperatures" during their first night in custody.

The family said they crossed the border on October 3, after making a "very brief detour on an unmarked road to avoid an animal on the road" that landed them in the United States.

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