Avery and Butterscotch’s room has scratching posts, carpeted cat trees and a three-tier hammock.

Avery, 3, likes to lounge on a tree near the window, watching people pass and curling his tail.

After moving in about a month ago, the feline pair and 12 other cats have made themselves at home.

The Animal Welfare League of Montgomery County, a nonprofit, no-kill cat shelter, has moved from a 12-cage, 600-square-foot building on Bonanza Way, near Snouffer School Road, to a mostly cageless, 2,100-square-foot, two-story townhouse on Park Avenue in Olde Towne Gaithersburg.

The shelter has six rooms and four bathrooms. Most cats either share a room with up to five other felines or are free to roam living areas. If they have had trouble adjusting or do not get along with other cats, they live in one of six cages. Sick cats are housed in an isolation room upstairs.

Colorful murals of paw prints and kittens brighten the walls. Litter boxes are hidden in corners, and a box of toys and balls overflows onto the hardwood floor.

The shelter’s goal is to create a relaxed, roomy environment for as many as 30 cats and the humans who adopt them, so people can get to know the cats’ personalities in a home setting, said Pat Gagne, the volunteer adoption coordinator at the shelter. Gagne said she has seen the cats grow calmer since moving out of their 3-by-3-by-6-foot cages.

The welfare league works with the Montgomery County Humane Society and owners who no longer can care for their cats to take in “adoptable” cats — meaning no trapped or feral animals, Gagne said.

This way, cats are adopted out of the shelter more quickly, so more can be shown; the average stay is less than six months.

Since its founding in 2005, the welfare league has saved almost 600 cats. Its old shelter began operations in 2007. Its 2011 budget is $100,000, coming mostly from grants and fundraisers, said Maureen Williams, the organization’s president.

The league is the only no-kill nonprofit shelter in the county; shelters that receive state funding must take all animals that need help and therefore must euthanize, Williams said. The league’s facility is the only cage-free shelter in the county she is aware of, although there are many in other states, she said.

Fourteen cats now live in the shelter, and 17 more are in short- or long-term foster homes.

The organization has more than 160 volunteers who visit for a few hours at a time, in one of two crews: one that cleans the shelter and make sure the cats have what they need, and one enrichment crew that plays with the cats and notes their behavior. The cats have volunteer visitors three times a day every day except Sunday. Adoption hours are Wednesday nights, Saturdays and some Sundays.

In a den upstairs, people considering adoption can sit on a recliner or couch and observe and play with a cat for as long as they want, Gagne said. Most of the furniture in the house has been donated by private owners, with some by organizations.

Volunteer counselors ask adopters questions such as how often they are home, if they have children and if they want a playful cat or one that will curl up on a lap, she said. The counselors then point them to a good fit.

Sometimes, it doesn’t take long to spot a perfect match, Gagne said.

After only a half-hour Sept. 10, Lorinda Potucek of Germantown walked out with Tigger. The 6-year-old, 22-pound, black-and-brown tabby jumped on her lap as soon as she sat down, Potucek said.

“Immediately, we connected, and he just would not get out of my lap,” said Potucek, who was the first person to adopt a cat from the new shelter.

Potucek and Tigger qualified for the shelter’s Senior to Senior program, which allows people over 60 to adopt a cat that is 6 or older for a discounted rate of $75; the normal cost is $125, and pairs are $200. Each cat is spayed or neutered upon entering the shelter, has current rabies and distemper vaccinations and has been tested for feline immunodeficiency virus and feline leukemia virus.

As a grand-opening special, all cats will be $50 next month. The house’s official grand opening is Sunday.

The welfare league also offers a low-cost spay and neuter program for cats and dogs, organized discussions about animal care and a monthly pet food bank.

The organization will rent the shelter for at least five years from Mary and Gustavo Amaro, who have used the building for office space since buying it eight years ago.

When Mary Amaro, a cat lover, heard the shelter wanted to move in, she thought it was great, she said.

The couple’s real estate agent cautioned them about the dangers of cats roaming the building, but they believe the welfare league is a good cause, Amaro said. The couple lowered the monthly rent from about $2,500 to about $2,000.

Avery can scamper upstairs, over the pipe cleaners that his roommate loves to play with, then snuggle on a sofa with someone who might want to take him home.

“It is nice to have cats living in that environment — it is beautiful,” Amaro said. “They are able to look out the windows and see nature — the squirrels and the birds.”