  Exotic superconducting properties of Sr$_{2}$RuO$_{4}$ have provided strong
support for an unconventional pairing symmetry. However, the extensive efforts
over the past decade have not yet unambiguously resolved the controversy about
the pairing symmetry in this material. While recent phase-sensitive experiments
using flux modulation in Josephson junctions consisting of Sr$_{2}$RuO$_{4}$
and a conventional superconductor have been interpreted as conclusive evidence
for a chiral spin-triplet pairing, we propose here an alternative
interpretation. We show that an overlooked chiral spin-singlet pairing is also
compatible with the observed phase shifts in Josephson junctions and propose
further experiments which would distinguish it from its spin-triplet
counterpart.
