We have studied the spin Hall magnetoresistance (SMR) arising at the interface of Pt and antiferromagnetic insulator MnTiO3 thin films. Using c axis oriented single-crystalline ilmenite-type MnTiO3 films on Al2O3 (0001) substrates grown by pulsed-laser deposition, we fabricated L-shaped multi-terminal Pt/MnTiO3 devices in which the longitudinal resistances of two orthogonally arranged channels can be simultaneously measured by the four-probe method. Magnetic field angular dependence of the magnetoresistance was consistent with symmetry relations for the SMR between spin-current polarization in Pt and magnetic moment in MnTiO3, evidencing the predominant SMR contribution. By utilizing distinct SMR responses of the two channels when a magnetic field was applied in parallel to one of the channels, we determined the Neél temperature (TN) to be 63 K in a 20-nm-thick MnTiO3 film, comparable to TN of a 40-nm-thick MnTiO3 film separately measured with a superconducting quantum interference device magnetometer. The electrically determined TN persisted down to the film thickness of 2.9 nm, indicating the robust antiferromagnetic ordering even at the surface of MnTiO3 ultrathin films.