Is the object a pulsar
As you said, the mass range of the object indicates that it could be a neutron star, rather than a black hole.
But also the density of the object is a clue. The density of a neutron star is much higher than that of a stable white dwarf.
Extremely regular electromagnetic pulses have to be observed. Known pulsars have a pulse period between 1.4 ms and 8.5 seconds. 
The wavelength of the pulses is in the radio range.
Pulsars slow down gradually, at a known rate, so you can measure how the pulse period evolves over time, and check that is compatible with the slow-down rate of a pulsar.


Adapted from this page