We present integral field spectroscopic observations with the Potsdam Multi Aperture Spectrophotometer of all 14 galaxies in the z \sim 0.1 Lyman Alpha Reference Sample ( LARS ) . We produce 2D line of sight velocity maps and velocity dispersion maps from the Balmer \alpha ( H \alpha ) emission in our data cubes . These maps trace the spectral and spatial properties of the LARS galaxies ’ intrinsic Ly \alpha radiation field . We show our kinematic maps spatially registered onto the Hubble Space Telescope H \alpha and Lyman \alpha ( Ly \alpha ) images . Only for individual galaxies a causal connection between spatially resolved H \alpha kinematics and Ly \alpha photometry can be conjectured . However , no general trend can be established for the whole sample . Furthermore , we compute non-parametric global kinematical statistics – intrinsic velocity dispersion \sigma _ { 0 } , shearing velocity v _ { \mathrm { shear } } , and the v _ { \mathrm { shear } } / \sigma _ { 0 } ratio – from our kinematic maps . In general LARS galaxies are characterised by high intrinsic velocity dispersions ( 54 km s ^ { -1 } median ) and low shearing velocities ( 65 km s ^ { -1 } median ) . v _ { \mathrm { shear } } / \sigma _ { 0 } values range from 0.5 to 3.2 with an average of 1.5 . Noteworthy , five galaxies of the sample are dispersion dominated systems with v _ { \mathrm { shear } } / \sigma _ { 0 } < 1 and are thus kinematically similar to turbulent star forming galaxies seen at high redshift . When linking our kinematical statistics to the global LARS Ly \alpha properties , we find that dispersion dominated systems show higher Ly \alpha equivalent widths and higher Ly \alpha escape fractions than systems with v _ { \mathrm { shear } } / \sigma _ { 0 } > 1 . Our result indicates that turbulence in actively star-forming systems is causally connected to interstellar medium conditions that favour an escape of Ly \alpha radiation .