Aslamazian, head of the Educated Media Foundation, formerly Internews Russia, fled the country last year after being charged with smuggling for failing to declare 9,550 euros ($12,400 at the time) at Sheremetyevo Airport in January 2007.
Travelers are permitted to bring any amount of cash into Russia, but amounts equivalent to more than $10,000 must be declared.
If customs officials decide that someone has brought a "large amount" of undeclared cash into the country, the traveler can be charged with smuggling.
Aslamazian's lawyer, Viktor Parshutkin, told the court Tuesday that the smuggling law was unconstitutional, because it gives no definition of a "large amount," meaning that authorities can arbitrarily decide whether to issue a misdemeanor or press smuggling charges.
Aslamazian, whose organization trained journalists, has said the case against her is linked to tightening state control over NGO activities in the country. She says she will not return to Russia until the case is dropped.
Smuggling is punishable by up to five years in prison, while a misdemeanor for bringing in more than $10,000 in undeclared cash can result in a fine of up to 2,500 rubles ($105).
The court is expected to issue a ruling before May 21, court spokeswoman Yekaterina Sidorenko said.
Parshutkin proposed that a new law be drawn up in which criminal charges would be pressed for smuggling cash or valuables worth more than $20,000.
Reached by telephone in Paris on Tuesday, Aslamazian said she had spoken with Parshutkin after the hearing and that what she "heard today gives me hope that this story can end positively."
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