Genevieve Sabourin was arraigned in a Manhattan court on Monday, a day after she was arrested on charges of stalking and aggravated harassment when Baldwin filed a complaint with police.
A judge released Sabourin, who has acted in television and film, on her own recognizance and issued a temporary order of protection for Baldwin, the Manhattan district attorney's office said.
Baldwin's publicist, Matthew Hiltzik, said, "As everyone knows, stalking is a serious issue, so we've turned this matter over to the New York Police Department."
Sabourin's attorney did not immediately return a phone call seeking comment after the arraignment.
On April 5, Sabourin showed up at the Lincoln Center for the Performing Arts, where Baldwin was hosting a screening of "Last Tango in Paris," and she had to be removed by security, police said.
She also is believed to have turned up unannounced at his home on Long Island on March 31 and to have gone to his address in lower Manhattan's Greenwich Village neighborhood while he wasn't there, authorities say.
The two met a decade ago on the set of "The Adventures of Pluto Nash," in which he had a cameo and she was a publicist.
According to authorities, the 54-year-old Baldwin told police that the 40-year-old Sabourin had been sending him emails for several weeks and that the notes were disturbing. She professed her love for him, begging to have his children and telling him to leave his wife, he said, according to police.
Baldwin recently became engaged to his 28-year-old girlfriend, Hilaria Thomas, a yoga instructor. Baldwin previously was married to actress Kim Basinger, and they have a daughter named Ireland.
In 2008, he published a book called "A Promise to Ourselves" about his personal experience dealing with divorce and his fight with Basinger over custody of their daughter.
Sabourin is a resident of Quebec. There was no answer to phone calls made to an address believed to be hers in a suburb outside Montreal.