Is seeking co-advising encouraged during Ph.D? I'm an undergraduate student about to apply for a Ph.D program this year. I am interested in knowing whether seeking co-advising from a related, but different department (in my case I'm applying for econometrics but thinking about looking for co-advising from the statistics department) is seen as a thing to be encouraged in graduate schools in the U.S., or is it considered a violation of the division of departments?

Also, would it make sense if I mention in my personal statement that one of the consideration of my applying for this school's economics department is that it also has a very good statistics department, from which I can potentially seek co-advising? Would the graduate admission committee be happy to see this kind of statements?
It is perfectly okay to have a co-adviser from another department. Econometrics and statistics are very close areas and often students pursuing PhD in Economics and Industrial Engineering (such as Reliability Analysis) have co-advisers from Statistics.

Often acceptance of an applicant in the program differs from department to department. However, you may mention an intention for collaborating with statistics department in the research statement. Also, if you do things appropriately you may have scope to get into the statistics department as a PhD student and pursue your research in light of economics. In other words, you may have greater chance of getting into the university as a PhD student. You may have to inquire about the possibility with the Statistics department. I guess you have good background in both statistics and economics so this seems to work out for you.