Splitting from one output to two inputs can usually be done without any noticeable loss of quality. I've done it myself, and it worked out well. I used a very short Y cable connector, so that the cables after the signal split were as short as possible.
Since this will affect the impedence ratios between your CD player and the next stage (the two inputs at the next stage together will result in a single, lower input impedence from the CD players perspective), you might benefit from a higher quality interconnect from the CD player to Y adapter. If the ratio of impedence from the CD player to the next component is too low, then cable capacitance will become an issue.
But only your ears will know for sure. A pair of gold connector Y adapter cables from Radio Shack won't cost you much to find out. You might have no need to change your ICs.
I assume the person asking the question cannot do whatever he needs to do with the outputs available on his CD player, hence the question
Martin pretty much covered the issues involved - putting two connections in parallel creates a harder load for the CD player to drive. This may or may not be an issue, depending on whether your CD player can handle the load, and that is determined by comparing the CD player's output impedance with the input impedance it needs to drive (in this case, the combination of the two destination devices in parallel).
This is assuming you're splitting an analog output. I do not know if a digital output (optical or coax) can be split or not.