This paper addresses the problem of distributed state estimation via multiple access channels (MACs). We consider a scenario where two encoders are simultaneously communicating their measurements through a noisy channel. Firstly, the zero-error capacity region of the general M-input, single-output MAC is characterized using tools from nonstochastic information theory. Next, we show that a tight condition to be able to achieve uniformly bounded state estimation errors can be given in terms of the channel zero-error capacity region. This criterion relates the channel properties to the plant dynamics. These results pave the way towards understanding information flows in networked control systems with multiple transmitters.