The novel coronavirus SARS-CoV-2 was first detected in the Pacific Northwest region of the United States in January 2020, with subsequent COVID-19 outbreaks detected in all 50 states by early March. To uncover the sources of SARS-CoV-2 introductions and patterns of spread within the United States, we sequenced nine viral genomes from early reported COVID-19 patients in Connecticut. Our phylogenetic analysis places the majority of these genomes with viruses sequenced from Washington state. By coupling our genomic data with domestic and international travel patterns, we show that early SARS-CoV-2 transmission in Connecticut was likely driven by domestic introductions. Moreover, the risk of domestic importation to Connecticut exceeded that of international importation by mid-March regardless of our estimated effects of federal travel restrictions. This study provides evidence of widespread sustained transmission of SARS-CoV-2 within the United States and highlights the critical need for local surveillance.