  X-ray and $\gamma$-ray observations by the Swift satellite revealed that a
fraction of tidal disruption events (TDEs) have relativistic jets. Jetted TDEs
have been considered as potential sources of very high-energy cosmic-rays and
neutrinos. In this work, using semi-analytical methods, we calculate neutrino
spectra of X-ray bright TDEs with powerful jets and dark TDEs with possible
choked jets, respectively. We estimate their neutrino fluxes and find that the
non-detection would give us an upper limit on the cosmic-ray loading factor,
$\xi_{\rm cr}\lesssim20$, for Sw J1644+57. We show that X-ray bright TDEs make
a sub-dominant ($\lesssim5-10$%) contribution to IceCube's diffuse neutrino
flux, and study possible contributions of X-ray dark TDEs given that particles
are accelerated in choked jets or disk-winds. We discuss future prospects for
multi-messenger searches of the brightest TDEs.
