It is written on page 12 of the datasheet:
It is possible to read the output registers (addresses 0x00 and 0x01) during a Temperature or Relative Humidity
measurement without affecting any ongoing measurement. Note that a write to address 0x00 or 0x01 while a
measurement is ongoing will abort the ongoing measurement.
But during testing, I was unable to achieve it. When HDC1080 is performing a measurement and the command to read the current address is issued, the write address (read operation) will return NACK.
So, how should this section in the datasheet be interpreted?