In the case of Clinton v. Jones (520 U.S. 681 (1997)), President Clinton claimed that, as a sitting
President, he could not be sued for civil litigation unrelated to his
office. However, the Supreme Court found that a sitting President has no immunity from civil law litigation against him, for facts unrelated to his office (having occurred before he took office).
Court ruled that separation of powers
does not mandate that Federal Courts delay all private civil lawsuits
against the President until the end of his term of office.
concurring opinion, it was argued that presidential immunity would
only apply if the President could show that a private civil lawsuit would
somehow interfere with the President's constitutionally-assigned duties.
"It appears to us highly unlikely to occupy any
substantial amount of petitioner's time."
the result of the suit, it can probably be argued by future Presidents
that this sort of civil litigation will interfere with their duties.