No, typically a decline will not negatively impact your score however the underlying reason why it declined, may.
Depending on the country, and how your credit score is calculated, it may include a large weighting on Capacity. Essentially how much of your available credit is being used. In some places, capacity can account for more than 25% of your score. Being over 70% of your overall credit capacity for any period of time, can be a bankruptcy indicator, thereby reducing your score.
As such, if you were declined due to being "Maxed Out" and that was the only revolving credit product you had... The decline doesn't hurt your score directly; the fact that you might be at 100% of your overall capacity could definitely hurt your score.