This paper introduces a digital-twin (DT)-assisted cooperative perception framework designed to improve perception accuracy under end-to-end (E2E) latency constraints and to balance perception accuracy and E2E latency under communication resource constraints in autonomous vehicles. We formulate an optimization problem that maximizes perception accuracy subject to latency and communication limitations, and solve it using a newly proposed coarse-to-fine search (CTFS) algorithm. Simulation results show that the proposed CTFS algorithm achieves 96.6% perception accuracy, close to exhaustive search, under latency constraints while reducing computational complexity by approximately 85.78%. The DT-assisted framework further achieves a 50% reduction in the non-DT communication cost through estimated, time-synchronized state updates.