The KATRIN experiment is the most precise setup for direct neutrino mass measurements. It is designed and optimised to measure the signature of the neutrino mass in the $\beta$-decay spectrum of tritium with a sensitivity of $0.2\,$eV$/$c$^2$ ($90\,\%$ C.L.).
In addition to the neutrino mass search, the measured $\beta$-spectrum can be analysed for an imprint of sterile neutrinos in the eV-range.
The first and second KATRIN science runs were taken in 2019. Between these two campaigns, the source activity was substantially increased, leading to improved constraints.
No sterile-neutrino signal was observed in the mass range up to $40\,$eV, and the exclusion contours improved, constraining the active-to-sterile mixing to $|U_{e4}|^2<6\times 10^{-3}$ ($95\,\%$ C.L.).
With analysis deeper into the spectrum, it is also possible to search for keV-scale sterile neutrinos. During the commissioning phase in 2018, a low source density allowed the opportunity to search for sterile neutrino masses up to $1.6\,$keV. From this data, mixing amplitudes of $|U_{e4}|^2<5\times 10^{4}$ ($95\,\%$ C.L.) are excluded. No sterile neutrino signature was found in the keV-range.