We present the first short-duration candidate microlensing events from the Kepler K2 mission. From late April to early July 2016, Campaign 9 of K2 obtained high temporal cadence observations over a 3.7 deg2 region of the Galactic bulge. Its primary objectives were to look for evidence of a free-floating planet (FFP) population using microlensing, and demonstrate the feasibility of space-based planetary microlensing surveys. Though Kepler K2 is far from optimal for microlensing, the recently developed mcpm photometric pipeline enables us to identify and model microlensing events. We describe our blind event-selection pipeline in detail and use it to recover 22 short-duration events with effective time-scales teff < 10 d previously announced by the OGLE and KMTNet ground-based surveys. We also announce five new candidate events. One of these is a caustic-crossing binary event, modelled in a companion study. The other four have very short durations (teff < 0.1 d) typical of an Earth-mass FFP population. Whilst Kepler was not designed for crowded-field photometry, the K2C9 data set clearly demonstrates the feasibility of conducting blind space-based microlensing surveys towards the Galactic bulge.