This is a hard one. I'm guessing that she probably did exactly what you said, she skimmed it to check and see if it was a suicide note. Since she's already a bit on edge about self-harm issues and your level of depression, I'd guess that as soon as she got the letter, she opened it with a bit of trepidation and concern in the pit of her stomach. Then when she got your message not to read the letter, she was stuck with, "Uh oh, I know that ilikecats is already questioning my trust and she's feeling betrayed because I sent the cops to pick her up. How do I handle this?" So maybe she hedged a bit.<<--how's that for mindreading
Truthfully, you probably will never know what went through her head or if she skimmed it or read it through--unless you bite the bullet and talk to her about what you're thinking and how you think she might have lied to you. It's okay to go in and say exactly what you said here. It's okay to tell her that you're struggling with trusting her and that you feel edgy and unsure about where the two of you stand on the issue of being honest with each other. This is the hardest part of therapy but it can be the most rewarding part. Believe me, I struggle with this part too, but when I go in and say what's going on in my head and checking with her what was going on in my therapist's head, it truly is the best stuff. It's how relationships that are solid, open and flow in both directions. I'm guessing that she's feeling a bit unsettled about how the connection between the two of you is going after the hospitalization incident. Go have a straight forward talk about what's going through your head. Believe me that's the only way you two are going to get through this very understandable period feeling of disconnection. Good luck!