This depends to a large degree on the locality in question.
In a small town in rural America, there is no need for the police to do anything in particular to be a part of the war on terror. Of course, if the police get any sort of information that might be related to terrorism, they should immediately inform those who are competent to deal with such things. However, it would be pointless to have local police in such areas train specially to deal with terrorism since the chances of them ever encountering it are minimal.
In a large city like New York City, it makes much more sense for local police to be more involved and to have more training in issues related to terrorism. With large immigrant populations, such cities are more likely to have people who might be interested in terrorism. With “high value” targets, such cities are also more likely to be attacked. Therefore, it makes sense to have police (at least some units, though probably not all officers) who are well-trained in detecting and investigating possible terrorists.