Finding an available on-street parking spot is a relevant problem of day-to-day life. In recent years, cities such as Melbourne and San Francisco deployed sensors that provide real-time information about the occupation of parking spots. Finding a free parking spot in such a smart environment can be modeled and solved as a Markov decision process (MDP). The problem has to consider uncertainty as available parking spots might not remain available until arrival due to other vehicles also claiming spots in the meantime. Knowing the parking intention of every vehicle in the environment would eliminate this uncertainty. Unfortunately, it does currently not seem realistic to have such data from all vehicles. In contrast, acquiring data from a subset of vehicles or a vehicle fleet appears feasible and has the potential to reduce uncertainty. In this paper, we examine the question of how useful sharing data within a vehicle fleet might be for the search times of particular drivers. We use fleet data to better estimate the availability of parking spots at arrival. Since optimal solutions for large scenarios are infeasible, we base our method on approximate solutions, which have been shown to perform well in single-agent settings. Our experiments are conducted on a simulation using real-world and synthetic data from the city of Melbourne. The results indicate that fleet data can significantly reduce search times for an available parking spot.