MIDTOWN, Manhattan (WABC) -- Police say a homeless man already in custody is now the main suspect in the death of a 59-year-old transgender woman in Chelsea.The 26-year-old man has been in police custody since last week, about an hour after the victim was found. He will now be questioned in her death.She was discovered unconscious on April 25 on Seventh Avenue, near the shelter where she had been staying.The woman, identified by police as Brenda Bostick, died Thursday at Bellevue Hospital, and her death was ruled a homicide.The homeless man, who has 28 prior arrests, appears to have been staying at the same shelter as the transgender woman. She was struck over the head during a dispute, authorities say.Detectives believe the two had stayed at the same Chelsea shelter -- Bowery Residence Committee, at 131 West 25th Street -- at some point in the past.Detectives are not investigating the death as a hate crime.The victim reportedly has a history of being in and out of the city's shelter system and was brought to the Bowery Residence Committee by the MTA's homeless outreach program in March.