The International Residential Code (IRC) is a little more lenient on the minimum specs for a Tiny House loft stairway than a regular house. Here’s their requirements:
• Stairway to loft must be minimum 17 inches in clear width at or above the handrail, and minimum width below handrail of 20 inches (AQ104.2.1.1).
• Minimum headroom is 6 feet 2 inches (IRC AQ104.2.1.2).
• Stair risers must be between 7 inches and 12 inches in height.
• Relation between riser height and tread width must be calculated using one of these two formulas: either the tread depth shall be 20 inches minus four-thirds of the riser height, OR riser height shall be 15 inches minus three-fourths of the tread depth (IRC AQ104.2.1.3).
• Stairs must meet the loft where the ceiling height is not less than 3 feet (IRC AQ104.2).
• The top tread and riser of a stairway to a loft must be constructed as a landing platform when the loft ceiling height is less than 6 feet 2 inches where stair meets loft. The landing platform should be minimum 20 inches in both width and depth, and the landing platform riser height to loft floor between 16 inches and 18 inches (IRC AQ104.2.1.5).
• Handrails and stair guards must meet same standards as regular residential construction (IRC R311.7.8 and R312.1) 

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Here’s some of our other articles about Tiny Houses:

• What is the code definition of a Tiny House?

• What is the code definition of a loft for a Tiny House?

• What is the code minimum size of a Tiny House loft? 

• What is the code minimum ceiling height of a Tiny House?

• What are the code requirements for emergency escape from a Tiny House loft?  

• What are the code requirements for a ladder to a Tiny House loft? 

• What are the code requirement for loft guard rails in a Tiny House?