In accreting young stars one of the prominent spectral features in the near infrared is the Paschen and Brackett series in emission. We examine hydrogen line ratios for 16 classical T Tauri stars from SpeX spectra and and assess the trends with veiling and accretion. The observed line ratios are compared to two theoretical models for line formation: (1) Baker and Menzel's (1938) Case B for radiative ionization and recombination and (2) a set of local line excitation calculations designed to replicate the conditions in T Tauri winds and magnetic accretion columns (Kwan & Fischer 2011). While the comparison between Case B and observed line ratios implies a wide range in electron density and temperature among the hydrogen line formation regions in T Tauri stars, the predictions of the local line excitation models give consistent results across multiple diagnostics. Under the assumptions of the local line excitation calculations, we find that n_H in the hydrogen line formation region is constrained to 2x10^10 -- 2x10^11 cm^-3, where stars with higher accretion rates have densities at the higher end of this range. Because of uncertainties in extinction, temperature is not well delineated but falls within the range expected for collisional excitation to produce the line photons. We introduce new diagnostics for assessing extinction based on near infrared hydrogen line ratios from the local line excitation calculations. ; Comment: Accepted by ApJ, 17 pages, 13 figures; v2 has some minor copyediting