There is no general answer. This strongly depends on the involved symmetry of ground and excited states and also whether you talk about resonant two-photon absorption or non-resonant two-photon absorption. As you are interested in conjugated molecules, you might want to have a look into the following works on polyenes:

http://scitation.aip.org/content/aip/journal/jcp/92/12/10.1063/1.458206

http://pubs.acs.org/doi/abs/10.1021/jp910010g

http://pubs.acs.org/doi/abs/10.1021/jz101409r

Dear Jan Philip Kraack ,

Thank you so much for your suggestion and I will try to understand based on the literature that you asked me to read because first time time I am trying to understand the link between normal absorption spectra and the two photon spectra.