Local incorporation is required for obtaining a licence to undertake financial institution businesses, which includes the activities of commercial banks, merchant banks, mortgage banks, post office savings banks, credit institutions, building societies, acceptance houses, discount houses, finance houses and any institution which by regulations is classified as a financial institution by the Central Bank.
"3. Interpretation
In this Act, unless the context otherwise requires—[...]
“company” means a company incorporated or registered under the Companies Act and includes—(a) the Uganda Development Bank established by the Uganda Development Bank Act; (b) a building society duly incorporated under the Building Societies Act; and (c) any institution classified as a financial institution under this Act;
“financial institution” means a company licensed to carryon or conduct financial institutions business in Uganda and includes a commercial bank, merchant bank, mortgage bank, post office savings bank, credit institution, a building society, an acceptance house, a discount house, a finance house or any institution which by regulations is classified as a financial institution by the Central Bank; 
“financial institution business” means the business of— (a) acceptance of deposits; (b) issue of deposit substitutes; (c) lending or extending credit, including— (i) consumer and mortgage credit; (ii) factoring with or without recourse; (iii) the financing of commercial transactions; (iv) the recovery by foreclosure or other means of amounts so lent, advanced or extended; (v) forfeiting, namely, the medium term discounting without recourse of bills, notes and other documents evidencing an exporter’ s claims on the person to whom the exports are sent; (vi) acceptance credits; (d) engaging in foreign exchange business, in particular buying and selling foreign currencies, including forward and option type contracts for the future sale of foreign currencies; ravell (e) issuing and administering means of payment, including credit cards,t ers’ cheques and banker’s draft (f) providing money transmission services; s; (g) trading for own account or for account of customers in— (i) money market instruments, including bills of exchange and certificates of deposit; (ii) debt securities and other transferable securities; (iii) futures, options and other financial derivatives relating to debt securities or interest rates; (h) safe custody and administration of securities; (i) soliciting of or advertising for deposits; (j) money broking; (k) financial leasing if conducted by a financial institution; (l) merchant banking; (m) mortgage banking; (n) creating and administration of electronic units of payment in computer networks; (o) dealing in securities business as an exempt dealer within the meaning of section 48 of the Capital Markets Authority Act; (p) transacting such other business as may be prescribed by the Central Bank. [...]
“foreign bank” means a body corporate or entity incorporated or formed under the laws of a country other than Uganda that— (a) is a bank according to the laws of any foreign country where it carries on business; [...]
“foreign company” means a company not being a local company; [...]
“local company” means a company registered or incorporated under the Companies Act in which the majority shares and actual controlling interest are held by citizens of Uganda; [...]
“non-bank financial institution” includes a credit institution,a building society, an acceptance house, a discount house and a finance house and any other institution classified by the Central Bank as a non-bank financial institution;
[...]
10. Application for a licence 
(1) A company proposing to transact or carry on business as a financial institution shall apply, in writing, to the Central Bank for a licence under this Act. [...]
(6) An application under subsection (1) of this section shall be accompanied by— (a) the applicant’s memorandum and articles of association or other instrument under which the company is incorporated, the certificate of incorporation and in the case of a person intending to conduct Islamic financial business, a statement stating that the business of the financial institution operations shall be conducted in accordance with the Shariah; (b) a certified copy of the resolution of the board of the applicant authorizing the preparation and submission of the application; (c) a sworn declaration for all individuals proposing to become directors, shareholders, controllers or managers, issued in a form specified by the Central Bank in regulations made under this Act. [...]" (Financial Institutions Act, 2004, as amended)
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"Part Ill—Licensing Procedures [...]
12. Information and supporting documents
1. Each application for a licence shall be accompanied by the following supporting documents— [...]
f) the Certificate of Incorporation;
g) the Memorandum and Articles of Association;
h) with respect to foreign applicants, a statement from the supervisory authority of the home country declaring that it has given prior approval or a “No objection” for the establishment of a subsidiary or any other office in Uganda, and that the applicant’s chairperson, directors, managers and substantial shareholders as a whole, are fit and proper persons within the meaning of the Act;[...]" (Financial Institutions (Licensing) Regulations, 2005)

Financial Institutions Act, 2004, as amended
Financial Institutions (Licensing) Regulations, 2005
[<a href="https://old.ulii.org/ug/legislation/act/2015/2004">Act</a>],[<a href="https://ulii.org/akn/ug/act/2016/2/eng@2016-02-04">Amend</a>],[<a href="https://old.ulii.org/ug/legislation/statutory-instrument/2005/41">Reg</a>]