The investigator found surveillance footage that showed Reyes at an ATM in the Manhattan at 2 a.m. on January 30.
Da Silva - who, according to CBS 2-NY was living in the USA illegally after overstaying a visa - was held without bail at the brief appearance.
Police arrested Javier de Silva, of Queens, New York, on Tuesday.
Police said they have examined hundreds of hours of surveillance footage in the case and interviewed several potential witnesses.
DeSilva was arrested after he fraudulently used an ATM card belonging to the victim, Valerie Reyes, Berry said.
"We are confident that the pursuit of justice for Valerie will be successful and we continue to work with the family to provide closure to this tragedy", Captain Berry, commander of the Greenwich Police Department detective division, said. William F. Sweeney Jr. said in a statement.
He was described as being cooperative during his interview.
Connecticut-based news journalist John Craven reported Da Silva admitted to his role in Reyes' death, telling investigators the pair had sex before "she fell to the floor and hit her head".
The suitcase was found on the side of a road in Greenwich, Connecticut.
Reyes, 24, went missing on January 29 from her home in New Rochelle, a small town in NY.
'She didn't mention anything or no one specific. They say he said he then tied her and put her in a suitcase. "I'm paranoid, mommy. I'm getting anxiety attacks.' She was having a hard time talking".
Reyes, a Barnes & Noble store clerk, had broken up with her boyfriend five days earlier, according to Sanchez.
"I asked her why do you feel this way?"
"She said, "Mami, his mother has cancer and I want to support him.' She was an angel like that", Reyes" mother, Norma Sanchez said.
"Reyes did tell her mother what turned out to be true: "'I'm afraid someone is going to murder me". Then on February 5, a red suitcase in the Town of Greenwich was found by a public works employee who, on unzipping the suitcase, discovered the body of Reyes inside.
Highway workers found her body in a wooded section of Greenwich, about 10 miles from New Rochelle.
The official cause of Reyes' death has not been confirmed as the autopsy is pending.
"We are, of course, devastated for my daughter's death, but I'm just beyond grateful that they found her murderer", her mother told reporters.
According to The Journal, Reyes had taken her iPad, iPhone, clothes and bed sheets with her when she disappeared.
A wake for Reyes is scheduled for this afternoon and evening at the Lloyd Maxie and Sons Funeral Home in New Rochelle.
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