Local authority is defined in clause (69) of section 2 of the CGST Act, 2017 and means the following: • a “Panchayat” as defined in clause (d) of article 243 of the Constitution; • a “Municipality” as defined in clause (e) of article 243P of the Constitution; • a Municipal Committee, a ZillaParishad, a District Board, and any other authority legally entitled to, or entrusted by the Central Government or any State Government with the control or management of a municipal or local fund; • a Cantonment Board as defined in section 3 of the Cantonments Act, 2006; • a Regional Council or a District Council constituted under the Sixth Schedule to the Constitution; • a Development Board constituted under article 371 of the Constitution; or • a Regional Council constituted under article 371A of the Constitution;
as per above State govt University is not a local authority
Refer question 4 of faqs. State govt University comes under authority of office of Governor.