Below are Mock-ups of the two choices to scope the search. The radio buttons would expose all choices initially. The drop-down search pattern I've seen more often, and I think users would be more familiar with it.
I think you should put them under "Advanced" search options. By default, you should search both options without forcing the user to choose either one (or select one from many). A good example is Google, there's one text field and a"search" button, that's it... advanced users can drill down themselves.
Dropdowns with just two values are an abomination (unto Nielsen). It's pretty hard to think of a use case where they would be justified. It is extremely frustrating to open a dropdown just to see that there's one more value in it. The reason you're usually seeing dropdowns in these contexts is that usually you have more than two options.
EDIT OK, it just occurred to me that maybe you didn't mean that there's only two options. In that case a good rule of thumb is to have a dropdown for 4 or more values. With three you can do it in either way, if you can arrange the layout for the radio buttons (it may be challenging).
If you only have these two options then this could be one way to do it (with the limited amount of context available). It mimics airline flight check-in forms I've seen.
The rationale I used: Give the user custom fields for each input type so they are less prone to making mistakes. For the SSN field it is also important to look "grown up" so that people trust you (unless they already completely trust your brand)
Instead of tabs you could also use radio buttons, if you wanted to.