Electron paramagnetic resonance (EPR) is used to investigate the triplet (S = 1) ground state of the neutral oxygen vacancy in bulk rutile TiO2 crystals. This shallow donor consists of an oxygen vacancy with two nearest-neighbor, exchange-coupled Ti3+ ions located along the [001] direction and equidistant from the vacancy. The spins of the two trapped electrons, one at each Ti3+ ion, align parallel to give the S = 1 state. These neutral oxygen vacancies are formed near 25 K in as-grown oxidized TiO2 crystals by illuminating with sub-band-gap 442 nm laser light. The angular dependence of the EPR spectra provides the principal values and axes for the g and D matrices. Observations of the Ti-47 and Ti-49 hyperfine lines when the magnetic field is along high-symmetry directions show that the two Ti3+ ions are equivalent; i.e., they have equal hyperfine A matrices. The A matrix for each Ti3+ ion in the neutral S = 1 oxygen vacancy is approximately half of the A matrix reported earlier for the one Ti3+ ion in the singly ionized S = 1/2 oxygen vacancy [Brant et al., J. Appl. Phys. 114, 113702 (2013)]. The neutral oxygen vacancies are thermally unstable above 25 K. They release an electron to the conduction band with an activation energy near 63 meV and convert to singly ionized S = 1/2 oxygen vacancies. When undoped TiO2 is sufficiently oxygen deficient (i.e., reduced), this combination of conduction band electrons and singly ionized oxygen vacancies may result in carrier-mediated ferromagnetism at room temperature.