Both Uses of

presume
in
The Scarlet Letter

Nevertheless, vixenly as she looks, many people are seeking at this very moment to shelter themselves under the wing of the federal eagle; imagining, I presume, that her bosom has all the softness and snugness of an eiderdown pillow.
p. 7.6

presume = assume

None of them, I presume, had ever read a page of my inditing, or would have cared a fig the more for me if they had read them all;
p. 26.6 *

Definitions:

(1) (presume as in: presumption of innocence)
to think of something as true or likely, even though it is not known with certainty

Something can be presumed because it seems reasonable or because there is a rule or law demanding such an assumption. For example, in the United States someone charged with a crime is presumed by law to be innocent unless they are proven guilty at a trial.
(2) (presumptuous as in: she is presumptuous)
exercising privileges to which one is not entitled -- such as being too familiar or too bossy