Sharing basic safety messages (BSMs) among connected vehicles (CVs) in a timely and reliable manner is of paramount importance in vehicular networks. When CVs are connected through ad hoc networks, the timely delivery of BSMs is very challenging due to the randomness in medium access control (MAC) and may lead to collision, especially in crowded networks. Besides, although the channel acquisition in conventional methods via transmission and reception of control signals results in collision-free message delivery, it adds high overhead cost. In this paper, we propose an efficient MAC scheme to carefully address these issues by improving communication efficiency and reducing the signaling overhead. The proposed scheme dedicates each time slot to only one CV and consequently is collision-free. Since BSMs contain similar information of a CV, we adopt the age of information (AoI) as the performance metric. We derive mathematical expressions for the MAC delay and AoI of the collision-free scheme by proposing a two dimensional Markov model. We compare the performance of proposed scheme with IEEE 802.11p standard and another lowcomplexity random scheme. AoI, delay, and collision rate are evaluated by OPNET network simulator, which provides realworld implementation scenario. Simulations results show that the collision-free scheme performs significantly better than IEEE 802.11p in highly congested networks. As an example, for a dense scenario where BSMs are generated every 10 ms, AoI of collisionfree scheme is about 50 ms while those of IEEE 802.11p and random scheme are about 140 and 150 ms, respectively, which are assumed too high for safety applications. Besides, the results show almost perfect match between mathematical derivations and results obtained by OPNET.