Finding a collision-free path for autonomous parking is usually performed by computing geometric equations, but the geometric approach may become unusable under challenging situations where space is highly constrained. We propose an algorithm based on Rapidly-Exploring Random Trees Star (RRT*), which works even in highly constrained environments and improvements to RRT*-based algorithm that accelerate computational time and decrease the final path cost. Our improved RRT* algorithm found a path for parallel parking maneuver in 95 % of cases in less than 0.15 seconds.