Investigation falls in Class 45, legal & security services, and depending on what exactly you sell it can also fall in Class 35 or Class 42 or Class 44. Everything below is read from the USPTO's own list of accepted descriptions, not from an opinion about where it belongs.
Searching the USPTO Trademark ID Manual for investigation returns 33 accepted descriptions, and most of them sit in Class 45. The manual is the list of identifications the office has already approved, so wording taken from it is pre-approved and settles the class at the same time.
The class follows from the identification you write, so "what class am I in" is really "what exactly do you sell". How the class system works covers the rest.
Legal, security, or personal and social services.
27 accepted descriptions in the manual mention investigation. For example:
You run a store, sell advertising or marketing, or provide business and office services.
3 accepted descriptions in the manual mention investigation. For example:
Software as a service (SaaS), app development, IT, design, or science and engineering services.
2 accepted descriptions in the manual mention investigation. For example:
Medical, dental, veterinary, wellness, beauty, grooming, or landscaping services.
1 accepted description in the manual mention investigation. For example:
Investigation appears in 4 classes because what you make, what it is made of and the service of selling it are separate classes. Pick the descriptions above that match what you actually do.
Investigation is a service, so it sits in Classes 35 to 45. Software that delivers a service is often Class 9 or Class 42 as well.
Legal, security and personal services: legal services are here. Commercial services are not, so retail store services and the rest of business support are Class 35.
The class decides what a registration covers; it does not decide whether the name is available. Relatedness is judged on the identifications, so a conflict can sit in a class you never looked at: the same name in a different industry.
Check whether your name is clear for investigation Searches the live USPTO register, including sound-alike and meaning-alike names. First search $2, then $5.Investigation sits in Class 45, legal & security services. That is where the USPTO's own ID Manual puts it: 27 accepted descriptions mentioning investigation fall in Class 45. Depending on exactly what you sell it can also fall in Class 35 or Class 42 or Class 44.
You file in every class you actually use the mark in, and the USPTO charges its fee per class. Selling a product and also running an online store for it is two classes, not one. Filing in classes you do not use is worse than filing in too few: an application has to be supported by real use or a genuine intent to use.
No. The class decides what a registration covers. Availability turns on whether someone already holds a similar mark for related goods, and relatedness is judged on what the identifications say rather than on the class number, so marks in different classes can still conflict.
Not what you sell? Search the class finder for your own wording, or browse all 45 classes.