A three-judge panel dismissed the motion from the bench immediately after hearing from the lawyers.
The court normally decides leave-to-appeal applications based on written documents.
The case involves a woman who was arrested at Vancouver airport in 2008 after a kilogram of methamphetamines was found hidden in a suitcase.
Jennifer Nagle had been pulled aside for a random screening by a border officer who questioned her about her travel plans and searched her purse before turning to the luggage.
The judge at her 2011 trial found that the officer should have advised Nagle of her rights before questioning her and acquitted her, a decision that was overturned by the provincial appeal court.
"She was not advised of these rights until after she had given incriminating answers that led to the formation of reasonable suspicion," the judge said.
The judge described the questioning and the purse search as "a trolling expedition" that ignored her charter rights.
The drug evidence was excluded and Nagle was acquitted.
Last September, the British Columbia Court of Appeal overturned that ruling and ordered a new trial, a decision Nagle sought to appeal to the Supreme Court.
The appeal justices said the trial judge was wrong to say the purse search by the border services officer violated Nagle's rights.
"With the information at hand, it was reasonable for him to detain her and for her luggage to be searched. The evidence to support that detention and the search and the evidence found as a result of the search was admissible.''
While there is some expectation of privacy at a border crossing, "no constitutional right to be free from the search of bags, purses, luggage or a pat down exists when one decides to cross a border."
Also on HuffPost