You raise an interesting question. Back in 1994, the American Heart Association Task Force on Cholesterol Issues put out a statement entitled "Very Low Cholesterol and Cholesterol Lowering" which noted that there is an increase in deaths from trauma, cancer, hemorrhagic stroke and respiratory and infectious diseases among those with total cholesterol levels less than 160 mg/dl. However, a substantial portion of those deaths seemed to be due to poor health unrelated to low cholesterol.
Since then, several studies have found a connection between low cholesterol and depression and anxiety. For example, results of a study in the Netherlands published in 2000 showed that middle-aged men with low cholesterol are more likely than other men to have symptoms of severe depression. An earlier study at found that healthy young women with cholesterol levels below 160 mg/dl were more likely to score high on measures of depression and anxiety than women with normal or high cholesterol. None of the women were being treated for depression or anxiety.
There is some evidence suggesting that having low cholesterol alters the way brain cells function and that brain cells with low levels of cholesterol may have fewer than normal receptors for the mood-elevating neurotransmitter serotonin which could lead to depression by preventing the cells from receiving and using this vital brain chemical. It's just one of many theories.
Two more recent studies have linked low cholesterol with an increased risk of suicide, depression, impulsivity and aggression. Here, researchers speculated that a decreased consumption of polyunsaturated fatty acids, especially omega-3s may be a risk factor and that increasing intake of foods high in omega-3 fatty acids might lower the risk. By the way, large trials of the statin drugs used to reduce cholesterol showed no increase in suicide among those participating, but then again it is unusual for people on statins to develop ultra low cholesterol..
These are all intriguing findings, but if you're not feeling depressed or anxious, there's probably no need to worry that your low cholesterol levels will lead you in that direction, and no other evidence that low cholesterol levels are unhealthy. However, as a precaution, you might want to increase your consumption of omega-3 fatty acids from flaxseed oil, sardines, salmon or other oily fish.