Yes you should take IELTS before applying but sometimes proof of your degree from US universities works as well. So be on safe side and NOT delaying your application process i would suggest you to take it before applying for it. Regarding your police report. any country you have lived for more than 6 months after 21 years of age, you need to furnish canadian immigration with  the police report. if you want more information go to following link

http://www.cic.gc.ca/english/immigrate/skilled/index.asp

Hope that answered your question