Seems to have been a Rep. held seat for a while, until Dems took it 2016. 2016 winner died in March.
Cavanaugh defeated the former incumbent seat holder.

Wahoo! Dems win big in yet another key special election, this one for New Hampshire’s 16th State Senate District https://t.co/vynqr1GIGs

— Daily Kos Elections (@DKElections) July 26, 2017

Dems in Disarray…. https://t.co/VL8YT4I901

— Eric Boehlert (@EricBoehlert) July 26, 2017