A chemical engineering student spent millions of dollars on handbags and luxury goods after a bank gave her the money by mistake, a Sydney court has heard.

Christine Jiaxin Lee, 21, was arrested at Sydney Airport on Wednesday night and appeared in Waverley Local Court on Thursday.

The court heard she was trying to board a flight to Malaysia using an emergency Malaysian passport.

According to the police prosecutor, the money was accessed through an overdraft facility, mistakenly attached to a Westpac savings account.

It is alleged Lee obtained $4.6 million fraudulently, $3.3 million of which has not been recovered.

The money was spent on luxury goods including handbags.

In addition to a charge of obtaining financial advantage by deception, she was also charged with knowingly dealing with proceeds of crime.

It's money we all dream about: magistrate

Magistrate Lisa Stapleton appeared to suggest the second charge might be more difficult to prove.

"It's not proceeds of crime, it's money we all dream about," Ms Stapleton said.

The court heard Lee had completed three years of a chemical engineering degree and had deferred her fourth year of study.

She has been living in Australia for the past five years and in March, a warrant was issued for her arrest.

Her boyfriend offered $1,000 in surety and agreed that she could live with him.

Her Malaysian passport has already been seized.

Ms Stapleton agreed to grant the woman bail on a number of conditions, including that she report to police twice a day.

The case will return to court at the Downing Centre on June 21.

Spending the money is a crime: police

Sydney City Police Detective Inspector Sean Heaney said if members of the public found money in their accounts that should not be there, or they had an ability to overdraw on an account that they should not have, they should not spend the money.

"Speak to your financial institution, have the matter rectified, if you fall into the temptation of spending other people's money, you may be committing criminal offences," Detective Inspector Heaney said.

"And it may be a matter of time before the police come knocking on your door."

He said exploiting an error made by the bank amounted to stealing.

"The money doesn't belong to you, you know that, don't go spending it, it's going to cause you some trouble with the police.

"It would be very tempting, a lot of people may succumb to that temptation.

"You should know what's in your account, if you realise there's something that doesn't belong to you, it will be identified, speak to them, do the right thing, get it cleared up as soon as possible."