The potentially hazardous asteroid (85990) 1999 JV6 has been a target of previously published thermal-infrared observations, and optical photometry. It has been identified as a promising candidate for possible Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect detection. The YORP effect is a small thermal-radiation torque attributed to be a key factor in spin-state evolution of small Solar System bodies. In order to detect YORP on 1999 JV6 we develop a detailed shape model and analyse the spin-state using both optical and radar observations. For 1999 JV6, we collected optical photometry between 2007 and 2016. Additionally, we obtained radar echo-power spectra and imaging observations with Arecibo and Goldstone planetary radar facilities in 2015, 2016, and 2017. We combine our data with published optical photometry to develop a robust physical model. We determine that the rotation pole resides at negative latitudes in an area with a 5{deg} radius, close to the south ecliptic pole. The refined sidereal rotation period is 6.536787+/-0.000007h. The radar images are best reproduced with a bilobed shape model. Both lobes of 1999 JV6 can be represented as oblate ellipsoids with a smaller, more spherical component resting at the end of a larger, more elongated component. While contact binaries appear to be abundant in the near-Earth population, there exists just a few published shape models for asteroids in this particular configuration. By combining the radar-derived shape model with optical light curves we determine a constant-period solution that fits all available data well. Using light curve data alone we determine an upper limit for YORP 8.5x10^-8^rad/day^2^. The bifurcated shape of 1999 JV6 might be a result of two ellipsoidal components gently merging with each other, or a deformation of a rubble pile with a weak-tensile-strength core due to spin-up. The physical model of 1999 JV6 presented here will enable future studies of contact binary asteroid formation and evolution.