Hi dpleft,
excited state dipole moments can be calculated using egrad. They are a "byproduct" of the excited state gradient (sharing some terms with them indeed). To obtain the dipole moment of the first excited state, modify your control file accordingly by adding $exopt 1, and then run egrad:
$lastdiag
$rpacor 400
$maxcor 500 MiB per_core
$dft
functional cam-b3lyp
gridsize m4
$soes all 1
$exopt 1
$rij
$cdspectrum nm
$spectrum nm
$subtitle
SP,DFT/no-RI,CAM-B3LYP,charge -1,cs,aug-cc-pVDZ,EX_STATE_VERTICAL_EXCITATION
$scfiterlimit 100
$coord file=coord
$scfconv 6
$grad file=gradient
$scfinstab rpas
$optimize
internal off
redundant off
cartesian on
global off
$symmetry cs
$tmole
$basis file=basis
$scfmo file=mos
$atoms
o 13-14 \
basis = o aug-cc-pVDZ
n 3,5 \
basis = n aug-cc-pVDZ
h 15-21 \
basis = h aug-cc-pVDZ
c 1-2,4,6-12 \
basis = c aug-cc-pVDZ
$scfdamp start=0.700 step=0.050 min=0.100
$operating system unix
$closed shells
a' 1-41 ( 2 )
a" 1-8 ( 2 )
$scfdump
$scfdiis
$scforbitalshift automatic=.1
$energy file=energy
$rundimensions
natoms=21
$end
Note that range-separated hybrids like CAM-B3LYP require the RI approximation in egrad, so I also added the $rij keyword. In the end of the calculation, the excited state dipole moment should then be reported in a very similar manner as for the ground state.
Best,
Christof