In a Startup does a Product Manager Need to be Technical?

You don't need to be a programmer, but it will be difficult to make proper decisions if you don't fully understand the tech and how long development takes. If you don't understand these things, the team of programmers in your startup will most likely end up being super frustrated with you, as you set unrealistic deadlines. So yeah, having some level of technical knowledge is preferred.

I'd agree with the comment above. I still think that even if you can't find/afford a technically skilled manager, involve this person into tech discussions/community as much as you can

A Product Manager must own/articulate/build the vision, craft the product roadmap, and research. Then this has to be oriented for stakeholders to get buy-in; which means being able to ELI5 complex topics. Knowing—at the very least—how to speak about the technical behind the conceptual is rare skill indeed, and would sit anyone at the top of my list in terms of being a Product Manager I would, personally, want to work with and under. Product Managers are on the strategic angle; they take ownership of the product's lifecycle, while Project Managers make sure milestones get hit in the appropriate windows for deliverables. If there's no technical knowledge, which it seems you're asking by the baseline question, how does one know the thing they're researching to be built, and communicating to stakeholders, can actually be achieved? I could be wrong, but strategy requires a deep investment in how things work. tldr; Yes, to answer your headline question. Not exactly, to answer the body content.

A product manager, in a startup or otherwise, needs to understand and be able to communicate with tech. You never have to have a degree in technology to be able to do that. You can always ask your team to explain stuff to you, including tech pieces (they're generally helpful people). If you still feel like you need to understand tech to feel comfortable, I'd say understand data flows - how does data flow end to end in your product, what systems does it go through, how do they change it. Understanding the data creation, processing, and storage process will make you very comfortable with tech.