Semantic Textual Similarity (STS) measures the degree of meaning overlap between two texts and underpins many NLP tasks. While extensive resources exist for high-resource languages, low-resource languages such as Kurdish remain underserved. We present, to our knowledge, the first Kurdish STS dataset: 10,000 sentence pairs spanning formal and informal registers, each annotated for similarity. We benchmark Sentence-BERT, multilingual BERT, and other strong baselines, obtaining competitive results while highlighting challenges arising from Kurdish morphology, orthographic variation, and code-mixing. The dataset and baselines establish a reproducible evaluation suite and provide a strong starting point for future research on Kurdish semantics and low-resource NLP.