Seeking undergrad research position at another university: is it OK to email PI and copy lab member? What if there's no response? I am an undergraduate research assistant in a laboratory at my school. Starting last year's fall semester through the summer and up to now, I have been working in the same laboratory, and I am hoping to gain additional knowledge, skills, and exposure by working in another research lab this summer. I have been looking for opportunities in different schools, but it appears that they encourage me to contact the labs directly. 

I am thinking about emailing the lab's PI and copying one of the lab members on the email. Is this an appropriate action as an undergraduate student seeking internship? Also, if I do not receive a response within a reasonable amount of time, is it okay to contact another member in the lab?
I suggest you contact the PI directly; I do not believe it is good to cc others on such emails unless you know someone already at this lab and you have told this person you will send an email.  The PI will eventually be in the loop and will presumably have to approve the position so emailing one and cc-ing another is in most cases tantamount just generating one extra email to delete.  (It may well be that the PI will pass it to someone else but that's internal and none of your business.)

If you don't get an answer, do not be insistent.  Senior researchers get 10s of such emails per week and there is no way they can answer all of them.  It's nothing personal, it's just a question of time management.

To improve your chances of your email being noticed, use for instance the subject line to refer to a recent paper by that lab and indicating in the email that your have read this paper and are interested in the topic etc.  This does not guarantee a reply but it will show you have done your homework to find what they do and it will increase the likelihood that your email will be read in full; avoid generic emails as people rarely read beyond the first two lines of emails explaining how honored you would be to work in group under such fantastic leadership.