Does a dominant or recessive allele cause severe combined immunodeficiency?

Not an easy answer: A person has two copies (or alleles) for each gene. One inherited from each parent. Dominant alleles are associated to clinical manifestations even when the other allele is normal. Two recessive alleles are needed to produce clinical manifestations. One recessive allele and one normal would result in a state called 'carrier', with no clinical symptoms.

It's complicated: In short, you ask a good question, but the answer is much more complicated. There are different types of severe combined immunodeficiency (scid). Some are autosomal, and some are x-linked. Many require homozygous changes, others can occur with genetic compounds. None are "autosomal dominant".