Witnesses told AFP that both bombings were suicide attacks by assailants on motorbikes, but there was no official confirmation.
A source familiar with the investigation said a Salafist movement in Gaza that sympathises with Islamic State group jihadists was suspected.
Hamas's interior ministry confirmed the three deaths, but spoke only of two "bombings" in Gaza City without providing details.
It had earlier said two officers died in "two explosions targeting police checkpoints" late Tuesday night, before revising the toll to three.
Suicide bombings are rare in the Gaza Strip.
In August 2017, a suicide bomber killed a Hamas guard in southern Gaza on the border with Egypt.
Hamas, itself an Islamist movement, has run the Gaza Strip since 2007 but has been regularly criticised by more radical Salafist groups in the impoverished, Israeli-blockaded coastal territory.