It followed a combination of the two. The British East India Company derived much of its power and legitimacy in places such as Bengal from holding powers granted to them from the Mughal empire or other local leaders by treaty. This lead to a dual court system of local and company courts that endeavored to apply Indian law to Indians and British law to its representatives and other Europeans. This system was a source of much confusion and injustice and contributed to criminality among Europeans. They could not be tried in Indian courts, and it was difficult for Indians to present their case in European courts. There was also a racial distinction that would remain for most of British India's history.

The Indian Mutiny would see the end of the Mughal Empire and the replacement of the East Indian Company with the British crown. Criminal and other law codes would be issued for a new court system and the Indian Civil Service to administer. These codes were heavily inspired by British Law, but would in many cases incorporate Hindu and Muslim law, and legal rulings would draw deeply on local traditions and customs if they could be proven to be ancient, and did not contradict other laws.

These only apply to the areas directly administered by the British. The Indian princely states, client kingdoms that had acknowledged first the EIC and then the British crown as their overlords. At the time of independence, there were some 565 different states. These states had a quasi-sovereignty, but the British were interested in guiding their legal development. The extent that these states operated independent law systems depended a lot on British policy, the character of the British resident, the individual ruler, and how secure British rule was felt to be at the time.

I hope this answers your question. Legal history can be a weird subject, and I hope my answer did it justice. It is not helped that the legal system in British India at all times seems to be a combination of pragmatism, idealism, and racism that created a complicated mess.

Sources:

Benton, Lauren. “From International Law to Imperial Constitutions: The Problem of Quasi-Sovereignty, 1870-1900.” Law and History Review 26, no. 3 (2008): 595–619.
“Brief History of Law in India « The Bar Council of India.” Accessed February 8, 2021. http://www.barcouncilofindia.org/about/about-the-legal-profession/legal-education-in-the-united-kingdom/.

Gilmour, David. The British in India: A Social History of the Raj. Illustrated edition. Farrar, Straus and Giroux, 2018.

GIUNCHI, ELISA. “The Reinvention of ‘Sharīʿa’ under the British Raj: In Search of Authenticity and Certainty.” The Journal of Asian Studies 69, no. 4 (2010): 1119–42.

Kolsky, Elizabeth. “Codification and the Rule of Colonial Difference: Criminal Procedure in British India.” Law and History Review 23, no. 3 (2005): 631–83.

Larby, C. J. B. “The Centenary of the High Courts of Calcutta, Bombay and Madras.” The International and Comparative Law Quarterly 12, no. 3 (1963): 1044–48.