River Song's sonic screwdriver was given to her by the Twelfth Doctor during their last date, on the Singing Towers of Darillium. Consistent with his memories, the screwdriver was the same model as what he previously possessed in his tenth incarnation.
It was the first gift the Doctor personally gave to River face-to-face, after seeing that she was using a sonic trowel, which he found "embarrassing". (TV: The Husbands of River Song)
Unbeknownst to her, this version included a neural relay (for the benefit of the Tenth Doctor), which would save her data ghost for uploading into the main computer of the Library. (TV: Forest of the Dead)
Among its functions, most of which were shared with the Doctor's screwdriver, River's screwdriver was capable of increasing the mesh densities of her expedition's suits to over 800%, (TV: Silence in the Library) activating and disabling the Library's gravity platforms, slowing the descent of a fall within a gravity well, fixing light bulbs and storing the consciousness of an individual held within its neural relay. (TV: Forest of the Dead)
The screwdriver was also fitted with dampers and a red setting, which made it more efficient than the Tenth Doctor's. (TV: Forest of the Dead) She told Helen Sinclair that it was better than the Doctor's. (AUDIO: The Sonomancer)