Police made the discovery at a property in Rosefield Street after being called to the address at 9pm on Sunday.
Officers initially treated the deaths as “unexplained” but confirmed on Monday that they were now regarding them as suspicious.
A man has been detained as part of the investigation, the force confirmed.
The block of flats has been cordoned off while officers investigate the deaths.
Police are also carrying out a review of CCTV and conducting house-to-house inquiries.
Detective Inspector Brian Geddes, who is leading the investigation, said: “I would be keen to hear from anyone who heard or saw anything suspicious in the Rosefield Street area, in the days between Thursday December 8 and Sunday December 11.”