Found Gray Cat on my Porch Last Night - Bellevue

I hope to find the owner in somehow, no tag on the collar. It’s a gray cat with a white bow collar, I think it’s a Chartreux Breed from the look. Came home last night and upon opening my porch door, it jumped in looking completely lost, walked into my apartment for a minute and went under the couch. This morning went out and then came back and went into my closet, so it might be its safest spot. Got in touch with my landlord but no luck as of yet through the FB neighborhood page and apartment management. It’s scared, but it did let me pet and was purring. Any other way I can find out? Please share.