Simply observe the same precautionary measures as in India. Keep your valuables in the hotel safety deposit locker, and when travelling never leave them unattended, avoid crowds of people.

Civil war and acts of terrorism ended in 2009. Though the Sri Lanka Army is engaged in clearing landmines, in former civil war areas better refrain from leaving frequently used roads and pathes.  

In general, threats to personal security for travellers in Sri Lanka are comparatively small. There has been an increase in violent crimes effecting tourists during the past few years, but they are still rare. India and Sri Lanka are much safer than most African, American or Southern European countries. For female travellers Sri Lanka can be considered to be safer than India, though sexual assaults against female tourists are increasing in recent time. Credit card cheating is less common than in India or Thailand, nevertheless you should prefer paying cash.

Scams involving gemstones occur often in Sri Lanka. Better you trust renowned institutes frequently visited by bus groups or those sellers recommended by the tour operator.

In touristic areas, at the Kandy lake close to the Tooth Temple in particular, be on guard for anybody  asking what is your country of origin, and then offering you unsolicited travel advice. Avoid to be accompanied and to accept those persons as guides, they will afterwards only push you to pay for services you did not ask for. Never believe them if they tell you the place you want to visit is closed now, less interesting, too dangerous, or located in a completely different direction, only in order to attract you to places of their own choice. Do not believe anyone who claims to be a professional (e.g. a tour guide, hotel receptionist, airline pilot), or in charge of a location (like a railway station) without producing a certificate. Be aware, someone expressing joy when telling to have met or seen you the day before in some restaurant or hotel or temple, is a lyer as long as you do not remember his face, and he will only try to ask for "help" for a serious private problem, meaning for your money, observing where you keep it. In tourist areas there are a lot of "teachers" and "welfare workers" or "deaf persons" begging for donations and showing photos or fake approvals of some institutions and lists of high amounts of previous donations. Be sure, they will only collect the money for themselves.

There is a special Tourist Police in Sri Lanka protecting and supporting foreign guests,
the Colombo contact number is 011 2382209.