Answer: No. It is not true.
Short explanation: Google autocomplete avoids suggesting the word "criminal" for any name, not just Hillary Clinton.
Here's the thing. The claim is not about search results. It's about autocomplete results. People are claiming that Google has manipulated the suggestions that show up when you type in "Hillary Clinton cri" -- for some reason, it doesn't complete to "criminal".
Apparently, the expectation is that if a search is popular, it should show up as a suggestion. This is not how it works: it's way more complicated. In particular, it is extremely important that autocomplete suggestions be heavily filtered for possibly-offensive content, because otherwise it would constantly be suggestion very offensive searches and you would not like that.
For example, imagine you just applied for jobs at a bunch of companies. Many of them will probably do a background check on you by searching for "<your name> criminal" on Google. If autocomplete really suggested the most popular searches, then after your job search, it might start suggesting "criminal" any time someone puts your name in, even though you aren't a criminal! How would you feel about that?
It is for exactly this sort of reason that Google heavily filters autocomplete suggestions. All other search engines have these kinds of filters too, although results will obviously vary. Remember, these are only suggestions. There is nothing stopping you from typing "criminal" yourself and completing the search.
Since you read this far, I will now reward you with a story.
Way back in 2006-ish, I was working on Google Search and observed this happen:
Ebay auto-generates Google search ads of the form "X for sale" (where X is your search term). One day, their system somehow came up with X = "African slaves", and thus they ran a Google ad for "African slaves for sale". Ouch.
Google, obviously, deleted the ad as soon as they saw it. However, before that happened, some people had seen the ad and wrote articles about it. So, now people who read the articles were trying to see the ad for themselves.
First they would type "African slaves", but the ad wasn't there. Trying harder, they would then type "African slaves for sale". Still no ad.
But then, some algorithm deep inside Google search said: "Hmm, when people search for 'African slaves', they often follow it by searching for 'African slaves for sale'."
And so, soon enough, when you searched for "African slaves", Google responded with: "Did you mean: 'African slaves for sale'?"
And that's why suggestions need to be filtered.
Disclaimer: I have not worked on Search since ~2009 and never worked specifically on autocomplete. The information in this post is based largely on common sense as informed by a background in the subject area, not on specific insider knowledge.