You'll be visited by Dr. Olga, who will check upon her patient and remind Kate of her current standing. Once she leaves the room, enter the balcony and approach the owl, who has returned carrying a fixed key. Return to the room and talk with Kurk, who will task you with bringing him his artificial leg. Make your way to the elevator and use the fixed key to unlock it. Interacting with the lift buttons will take you to the ground floor (you'll also be rewarded with an achievement - Respect for Protocol).
Once you've turned up on the ground floor, approach the front office. Talk to the lady at the counter to receive directions to Dr. Zamiatin's office. There is a small opening between the both sides of the wall on the other side of the counter (screenshot above) - use it. Use the door found before two plus-sized women to enter the study. The conversation with Dr. Zamiatin will go smooth, as it turns out that he'll allow Kate to leave the facility if she manages to get the necessary permission from Dr. Olga. Moreover, you'll receive a book describing the Jukolians. Ask him about the subject and use all of the dialogue options.
You can also look through the book. To do so, press "J" to open the document inventory. Then, press 3 to enter a close-up of the book, press 2 to translate the given page (the book is in Russian) press 4 to return to the close-up, and press the right directional button to move to the next page. Use the opportunity to read the whole book.