The detection of family relationships in genetic databases is of interest in various scientific disciplines such as genetic epidemiology, population and conservation genetics, forensic science, and genealogical research. Nowadays, screening genetic databases for related individuals forms an important aspect of standard quality control procedures. Relatedness research is usually based on an allele sharing analysis of identity by state (IBS) or identity by descent (IBD) alleles. Existing IBS/IBD methods mainly aim to identify first-degree relationships (parent-offspring or full siblings) and second degree (half-siblings, avuncular, or grandparent-grandchild) pairs. Little attention has been paid to the detection of in-between first and second-degree relationships such as three-quarter siblings (3/4S) who share fewer alleles than first-degree relationships but more alleles than second-degree relationships. With the progressively increasing sample sizes used in genetic research, it becomes more likely that such relationships are present in the database under study. In this paper, we extend existing likelihood ratio (LR) methodology to accurately infer the existence of 3/4S, distinguishing them from full siblings and second-degree relatives. We use bootstrap confidence intervals to express uncertainty in the LRs. Our proposal accounts for linkage disequilibrium (LD) by using marker pruning, and we validate our methodology with a pedigree-based simulation study accounting for both LD and recombination. An empirical genome-wide array data set from the GCAT Genomes for Life cohort project is used to illustrate the method.