Given that the Indian Penal Code wasn't introduced until 1860 and then later the Punjab Laws Act of 1872 I am trying to gain a better understanding of the laws governing the Punjab under British rule during the Board of Administration between 1849 and 1853.
A Journal article titled "Development of Civil Service Punjab and Haryana (1849 - 1919)" noted that the newly annexed "territory was to be treated as a Non-Regulation Province" which meant "the civil service of the Punjab was not governed by any Act of the British Parliament or the Regulations of the Government of India." Instead it was "placed under the charge of a 'Board of Administration'".
In 1883 R. Bosworth Smith wrote (Page 252) on whether the Punjab was governed as a military government or by the East India Company he wrote "Neither, and yet both. Both, that is, in part".
To figure out who was in control of what Smith writes (Page 292) that Sir Henry Lawrence was President of the Board and "medium of communication with the Supreme Government" which was another name for the Indian Government. At the time, this would have meant the Board communicated with the East Indian Company which would have been under the Government of India Act 1833.
Despite communicating with the East India Company this appears to have been for shared objectives since another journal article titled "Institutional Development of Legislation in Punjab 1849-1947: An Historical Analysis" went as far to say that the Board "possessed absolute and supreme executive, military and judicial powers and unobstructed control all over matters regarding Punjab."
To figure out the specifics of what that meant Smith continues by saying Sir Henry Lawrence (Page 292) "was to be the head of the executive in all its branches, to take charge of the political relations with the adjoining states, to have the general control of the frontier force, of the Guide corps, of the military police, and of the Civil Engineer's department".
I found information on the "frontier force" (Punjab Irregular Force) and the "Guide corps" (Corps of Guides) but I assume the "Civil Engineer's department" was part of the East India Company. When it comes to the military police I assume that simply meant an armed police force which was created by the Board and was not part of the East India Company.
A journal article on the "Administrative Evolution of the Punjab and British Rule (1849-1859)" goes into further detail how the Board created Military Police that would be able to arrest people and present them in front of a court: "An armed Police Force, foot and horse was raised and partially organised, both for the protection of the Frontier and the preservation of internal peace. Civil and Criminal courts were established offenders were seized, and during the course of the year 8000 convicts were lodged in custody."
The journal article then goes on to describe how the Board then created commissioned officers with criminal and civil powers: "All officers were vested with triple powers, criminal, civil and fiscal. The commissioners were to be Superintendents of revenue and police, and to exercise the legal proceedings of a civil and the criminal powers of a Session's Judge."
Smith writes (Page 271) that for local matters Tahsildars were used as judges "of local matters of small importance, were confirmed in their judicial as they had already been in their police authority". This suggests there were laws the Board wanted to enact but left local laws in the villages alone.
The extent this is held true is unknown, Wikipeda refernces a book by Arvind-Pal Singh Mandair that states (Page 77) that the "Board maintained a strict policy of ‘non-interference’, or what amounted to secular governance, in regard to religious and cultural matters." That book in turn references "Imperial Encounters: Religion and Modernity in India and Britain" by Peter van der Veer that simply states (Page 21) "The government of Madras was forced by the anti-idolatry activists to retreat from their policies and accept a new policy of 'noninterference,' made into law in 1863." The author was most likely referring to The Religious Endowments Act, 1863 which obviously happened after the Board Administration and gives no mention of the Board itself.
An example of interference before the Board was created was by a Board member, John Lawrence, who was the Commissioner of the Tans-Sutlej States and in 1846 he wrote (Page 186) "proclamations and letters to all the chiefs" that practices such as "infanticide, suttee, and the destruction of leprous persons by burying them alive or throwing them into water" were met with "the severest penalties". Later these states became part of the Punjab province that the Board governed.
That's my attempt at trying to understand how things were governed and who was responsible but it says nothing about what laws were used. Were laws passed down from the East India Company, were proclamations created before the Board kept, were the courts based on English law, was there a High and Supreme Court?