Rotational levels of molecular free radicals can be tuned to degeneracy using laboratory-scale magnetic fields. Because of their intrinsically narrow width, these level crossings of opposite-parity states have been proposed for use in the study of parity-violating interactions and other applications. We experimentally study a typical manifestation of this system using 138 BaF. Using a Stark-mixing method for detection, we demonstrate level-crossing signals with spectral width as small as 6 kHz. We use our data to verify the predicted lineshapes, transition dipole moments, and Stark shifts, and to precisely determine molecular magnetic g-factors. Our results constitute an initial proof-ofconcept for use of this system to study nuclear spin-dependent parity violating effects.PACS numbers: 32.80. Ys, 12.15.Mm, 21.10.Ky It has been suggested that diatomic molecules could be used as a system to measure classes of parity-violating (PV) electroweak interactions that are difficult to access through other means [1][2][3]. The level structure of diatomic free radicals systematically makes it possible to tune states of opposite parity to near degeneracy, using a magnetic field such that the Zeeman shift of the electron spin matches the rotational splitting. Near such a level crossing, the mixing of these long-lived states due to nuclear spin-dependent (NSD) PV interactions is greatly enhanced [4]. This should make it feasible to measure small, poorly understood effects such as those due to nuclear anapole moments and axial hadronic-vector electronic electroweak couplings [3,5,6]. This type of level crossing has also been identified as an attractive system for quantum simulations of conical intersections [7] or magnetic excitons [8], and for sensitive detection of electric fields [9].Here we report an experimental study of Zeeman-tuned rotational level crossings in 138 BaF. Using an electric field pulse to induce transitions between the near-degenerate levels, we demonstrate the ability to understand and control the system with energy resolution at the kHz scale, as desired for the measurement of nuclear spin-dependent PV effects in similar systems. By measuring the magnetic field at several crossings, we extract precise values for poorly known magnetic g-factors; also, by studying transfer efficiency vs. electric field, we deduce values for electric dipole matrix elements between the crossing levels, and for off-resonant Stark shifts not previously con- * e-mail: sidney.cahn@yale. 138 Ba is spinless. In the absence of external fields, the lowest energy levels are described by the Hamiltonianwhere N is the rotational angular momentum, S = 1/2 is the electron spin, and n is a unit vector along the internuclear axis ( = 1 throughout) [11,12]. All parameters of H 0 have been precisely measured [13][14][15]. The rotational constant B is much larger than the spin-rotation (SR) constant γ, the hyperfine (HF) constants b and c, and the centrifugal correction constant D; thus N is a good quantum number, with eigenstates of energ...