I can't think of any examples of 'I'm responsible to..' But 'I'm responsible for my children's education' 'the government is responsible for the crisis' etc.

If you are responsible for something, that is your area, or your job. If you are responsible to someone, that is your boss or supervisor.

i found this: http://learnersdictionary.com/qa/What-preposition-should-be-used-after-responsible- and this: https://www.btb.termiumplus.gc.ca/tpv2guides/guides/wrtps/index-eng.html?lang=eng&lettr=indx_catlog_r&page=9Z4eEDsqjvuA.html