\version "2.12.0"  % necessary for upgrading to future LilyPond versions.

\header{
  title = "Example"
}


upper = \relative c' {
\clef treble
\key c \major
\time 3/4

c8. c16 c8 c8 c8 c8 ~ %How to apply this legato to the next c2?

<<
{ c2. }
\\
{ r8 a16 a a8 a8 a4 }
>>


}

lower = \relative c {
\clef bass
\key c \major
\time 3/4

r2. r2.

}

\score {
\new PianoStaff <<
\set PianoStaff.instrumentName = #"Piano "
\new Staff = "upper" \upper
\new Staff = "lower" \lower
>>
\layout { }
\midi { }
}