To achieve resource-efficient hardware designs, high-level synthesis (HLS) tools share (i.e., time-multiplex) functional units among operations of the same type. This optimization is typically performed in conjunction with operation scheduling to ensure the best possible unit usage at each point in time. Dataflow circuits have emerged as an alternative HLS approach to efficiently handle irregular and control-dominated code. However, these circuits do not have a predetermined schedule-in its absence, it is challenging to determine which operations can share a functional unit without a performance penalty. More critically, although sharing seems to imply only some trivial circuitry, time-multiplexing units in dataflow circuits may cause deadlock by blocking certain data transfers and preventing operations from executing. In this paper, we present a technique to automatically identify performance-acceptable resource sharing opportunities in dataflow circuits. More importantly, we describe a sharing mechanism which achieves functionally correct and deadlock-free dataflow designs. On a set of benchmarks obtained from C code, we show that our approach effectively implements resource sharing. It results in significant area savings at a minor performance penalty compared to dataflow circuits which do not support this feature (i.e., it achieves a 64%, 2%, and 18% average reduction in DSPs, LUTs, and FFs, respectively, with an average increase in total execution time of only 2%) and matches the sharing capabilities of a state-of-the-art HLS tool.