Is my homeowners association responsible for attic rat infestation?

They may not be responsible in that they may not have been the source of the rats.

Ask your board for attention to pests in the attic. The attic may be common area, limited common area, or part of your home/ unit. Your governing documents detail these boundaries.

Then, you can work with the board to remove the pests and remove access to the attic to prevent any further infestation.