Municipal governments are beginning to confront the growing pension liabilities; this leads local politicians throughout the country to become increasingly vocal about restraining costs and limiting services.
the growing pension liabilities; this leads
their growing pension liabilities; leading
the growth in their pension liabilities, which leads
their growing pension liabilities, leading
their growing pension liabilities, that leads
After reviewing the question, I went with (D).
In (A), it's not really clear what "this" is referring to. At least I didn't feel convinced with what "this" means.
In (B), the usage of semicolon is incorrect. A semicolon is used to separate two independent clauses, but have some sort of connection with each other. Each sentence should be able to stand alone. However, with the semicolon separating these two sentences, the second sentence cannot stand alone because it lacks a subject.
In (C), I believe there's a subject/verb agreement error. The word "leads" after which should be "lead", since the "which" sentence is modifying a plural noun - liabilities.
In (D), everything's fixed, with "leading..." modifying the previous sentence.
In (E), the usage of comma + that is awkward and unnecessary. Again, the word "leads" should be "lead".
This is my own opinion. What's the OA?