This is "A Little Intelligence" (1958) by Randall Garrett and Robert Silverberg.
The story takes place during a peace conference of the Pogatha from Capella IX; they are being hosted in a cathedral since it is the place where Earth Government believes they will learn the least useful information about Earth and its technology. The protagonist is Sister Mary Magdalene.
"Vor Gontakel!" the Major said sharply. "What would you say if I told you that another cat at the far end of the corridor saw you stab Vor Nollig and burn down Felicity?"
Vor Gontakel looked perfectly unruffled and unperturbed. No Earthman's bluff was going to get by her! "I would say the cat was lying."
The reason it worked:
"Sister Elizabeth," the nun said. "She told me that Felicity had been murdered. And she had been — murdered, I mean, not just 'killed.' Vor Gontakel saw me talking to the cat, and heard Felicity meow back. How was she to know that the cat wasn't intelligent? She knew nothing about Terrestrial life. The other two did.
Vor Gontakel and Vor Nollig are members of different factions of the peace delegation, and Vor Gontakel's faction wished to cause the peace talks to fail in order to retain their position at the top of the power structure on their world, a position that would be threatened by peace.